- published: 30 Jul 2021
- views: 86699
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Dynamical system (definition)
The dynamical system concept is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space. The concept unifies very different types of such "rules" in mathematics: the different choices made for how time is measured and the special properties of the ambient space may give an idea of the vastness of the class of objects described by this concept. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the ambient space may be simply a set, without the need of a smooth space-time structure defined on it.
Formal definition
There are two classes of definitions for a dynamical system: one is motivated by ordinary differential equations and is geometrical in flavor; and the other is motivated by ergodic theory and is measure theoretical in flavor. The measure theoretical definitions assume the existence of a measure-preserving transformation. This appears to exclude dissipative systems, as in a dissipative system a small region of phase space shrinks under time evolution. A simple construction (sometimes called the Krylov-Bogolyubov theorem) shows that it is always possible to construct a measure so as to make the evolution rule of the dynamical system a measure-preserving transformation. In the construction a given measure of the state space is summed for all future points of a trajectory, assuring the invariance.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Dynamical_system_(definition)
Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.
At any given time a dynamical system has a state given by a set of real numbers (a vector) that can be represented by a point in an appropriate state space (a geometrical manifold). The evolution rule of the dynamical system is a function that describes what future states follow from the current state. Often the function is deterministic; in other words, for a given time interval only one future state follows from the current state; however, some systems are stochastic, in that random events also affect the evolution of the state variables.
Overview
The concept of a dynamical system has its origins in Newtonian mechanics. There, as in other natural sciences and engineering disciplines, the evolution rule of dynamical systems is an implicit relation that gives the state of the system for only a short time into the future. (The relation is either a differential equation, difference equation or other time scale.) To determine the state for all future times requires iterating the relation many times—each advancing time a small step. The iteration procedure is referred to as solving the system or integrating the system. If the system can be solved, given an initial point it is possible to determine all its future positions, a collection of points known as a trajectory or orbit.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Dynamical_system
Dynamical systems theory
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a cantor set—one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations.
This theory deals with the long-term qualitative behavior of dynamical systems, and studies the nature of, and when possible the solutions of, the equations of motion of systems that are often primarily mechanical or otherwise physical in nature, such as planetary orbits and the behaviour of electronic circuits, as well as systems that arise in biology, economics, and elsewhere. Much of modern research is focused on the study of chaotic systems.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Dynamical_systems_theory
Podcasts:
-
The Anatomy of a Dynamical System
Dynamical systems are how we model the changing world around us. This video explores the components that make up a dynamical system. Follow updates on Twitter @eigensteve website: eigensteve.com This video was produced at the University of Washington
published: 30 Jul 2021 -
Inside Dynamical Systems and the Mathematics of Change
Bryna Kra searches for structures using symbolic dynamics. “[I love] finding order where you didn’t know it existed,” she said. "This is how I think about math: It’s about how things fit together." Read the full story at Quanta Magazine: https://www.quantamagazine.org/bryna-kra-searches-symbols-for-the-rules-of-change-20201117/
published: 17 Nov 2020 -
5.1 What is a Dynamical System?
Unit 5 Module 1 Algorithmic Information Dynamics: A Computational Approach to Causality and Living Systems---From Networks to Cells by Hector Zenil and Narsis A. Kiani Algorithmic Dynamics Lab www.algorithmicdynamics.net
published: 26 Aug 2018 -
Topics in Dynamical Systems: Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos
This video provides a high-level overview of dynamical systems, which describe the changing world around us. Topics include nonlinear dynamics, linearization at fixed points, eigenvalues and eigenvectors, bifurcations, invariant manifolds, and chaos!! @eigensteve on Twitter eigensteve.com databookuw.com This video was produced at the University of Washington %%% CHAPTERS %%% 0:00 Introduction 4:35 Linearization at a Fixed Point 9:37 Why We Linearize: Eigenvalues and Eigenvectors 14:46 Nonlinear Example: The Duffing Equation 19:59 Stable and Unstable Manifolds 21:12 Bifurcations 25:20 Discrete-Time Dynamics: Population Dynamics 27:02 Integrating Dynamical System Trajectories 29:07 Chaos and Mixing
published: 16 Jan 2023 -
Introduction to System Dynamics: Overview
MIT 15.871 Introduction to System Dynamics, Fall 2013 View the complete course: http://ocw.mit.edu/15-871F13 Instructor: John Sterman Professor John Sterman introduces system dynamics and talks about the course. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
published: 28 Jul 2014 -
Dynamical Systems Introduction
Find the complete course at the Si Network Platform → https://tinyurl.com/4n89knfk Dynamical systems is a area of mathematics and science that studies how the state of systems change over time, in this module we will lay down the foundations to understanding dynamical systems as we talk about phase space and the simplest types of motion, transients and periodic motion, setting us up to approach the topic of nonlinear dynamical systems in the next module. Within science and mathematics, dynamics is the study of how things change with respect to time, as opposed to describing things simply in terms of their static properties the patterns we observe all around us in how the state of things change overtime is an alternative ways through which we can describe the phenomena we see in our worl...
published: 10 Apr 2015 -
Chaos Theory: the language of (in)stability
The field of study of chaos has its roots in differential equations and dynamical systems, the very language that is used to describe how any physical system evolves in the real world. This video aims to tell the story of chaos step by step, from simple non-chaotic systems, to different types of attractors, to fractal spaces and the language of unpredictability. Timestamps: 00:00 - Intro 02:17 - Dynamical Systems 04:11 - Attractors 06:28 - Lorenz Attractor: Strange 08:54 - Lorenz Attractor: Chaotic Music by: Karl Casey @ White Bat Audio https://www.youtube.com/watch?v=Gao-DHIyj0Q&ab_channel=WhiteBatAudio https://www.youtube.com/watch?v=2gsn1HrDtdI&ab_channel=WhiteBatAudio https://www.youtube.com/channel/UC_6hQy4elsyHhCOskZo0U5g LAKEY INSPIRED https://soundcloud.com/lakeyinspired https://...
published: 18 May 2021 -
Chaos: The Science of the Butterfly Effect
Chaos theory means deterministic systems can be unpredictable. Thanks to LastPass for sponsoring this video. Click here to start using LastPass: https://ve42.co/VeLP Animations by Prof. Robert Ghrist: https://ve42.co/Ghrist Want to know more about chaos theory and non-linear dynamical systems? Check out: https://ve42.co/chaos-math Butterfly footage courtesy of Phil Torres and The Jungle Diaries: https://ve42.co/monarch Solar system, 3-body and printout animations by Jonny Hyman Some animations made with Universe Sandbox: https://universesandbox.com/ Special thanks to Prof. Mason Porter at UCLA who I interviewed for this video. I have long wanted to make a video about chaos, ever since reading James Gleick's fantastic book, Chaos. I hope this video gives an idea of phase space - a pictu...
published: 06 Dec 2019 -
WG Virtual Seminars, Hypothalamic-Pituitary-Adrenal Axis Dynamics, Vukojevic, October 17, 2024
Quenching Small-Amplitude Limit Cycle Oscillations for Predictive Modeling of Complex Molecular Mechanisms Underlying Chemical and Biochemical Oscillatory Reactions. Insights into the Effects of Ethanol on Hypothalamic-Pituitary-Adrenal (HPA) Axis Dynamics Vladana Vukojevic, PhD Karolinska Institute Quenching Small-Amplitude Limit Cycle Oscillations, i.e., Quenching Analysis (QA), is a method specifically designed to take the advantage of the oscillatory dynamics that emerges in the vicinity of a supercritical Hopf bifurcation and harvest it to acquire unique quantitative information about the investigated system that can easily be compared with model predictions. To this aim, QA relies on a series of controlled additions of a compound that is inherent to the system or reacts with a react...
published: 18 Oct 2024 -
Dynamical Systems Theory - Motor Control and Learning
Dynamical Systems Theory - Motor Control and Learning: Dynamical systems theory, Dynamical pattern theory, Coordination dynamics theory, Ecological theory, Action theory, Multidisciplinary perspective, Physics, Biology, Chemistry, Mathematics, Human movement control, Nonlinear dynamics, Boiling water, Variable, Nonlinear behavioral change, Human coordinated movement, Coordination patterns, Speed, Dynamics, Stability, Attractors, Attractor state, Energy-efficient, Walking gait, Running gait, Speed of locomotion, Order parameters, Collective variables, Relative phase, Rhythmic movement, In-phase, Antiphase, Control parameter, Self-organization, Hurricanes, Coordinative structures, Ensemble of muscles and joints, Muscle synergies, Motor synergies, Intrinsic coordinative structures, Developed ...
published: 21 Jul 2022
developed with YouTube
17:53
The Anatomy of a Dynamical System
- Order: Reorder
- Duration: 17:53
- Uploaded Date: 30 Jul 2021
- views: 86699
Dynamical systems are how we model the changing world around us.
This video explores the components that make up a dynamical system.
Follow updates on Twi...
Dynamical systems are how we model the changing world around us.
This video explores the components that make up a dynamical system.
Follow updates on Twitter @eigensteve
website: eigensteve.com
This video was produced at the University of Washington
https://wn.com/The_Anatomy_Of_A_Dynamical_System
Dynamical systems are how we model the changing world around us.
This video explores the components that make up a dynamical system.
Follow updates on Twitter @eigensteve
website: eigensteve.com
This video was produced at the University of Washington
2:10
Inside Dynamical Systems and the Mathematics of Change
- Order: Reorder
- Duration: 2:10
- Uploaded Date: 17 Nov 2020
- views: 41477
Bryna Kra searches for structures using symbolic dynamics. “[I love] finding order where you didn’t know it existed,” she said. "This is how I think about math:...
Bryna Kra searches for structures using symbolic dynamics. “[I love] finding order where you didn’t know it existed,” she said. "This is how I think about math: It’s about how things fit together." Read the full story at Quanta Magazine: https://www.quantamagazine.org/bryna-kra-searches-symbols-for-the-rules-of-change-20201117/
https://wn.com/Inside_Dynamical_Systems_And_The_Mathematics_Of_Change
Bryna Kra searches for structures using symbolic dynamics. “[I love] finding order where you didn’t know it existed,” she said. "This is how I think about math: It’s about how things fit together." Read the full story at Quanta Magazine: https://www.quantamagazine.org/bryna-kra-searches-symbols-for-the-rules-of-change-20201117/
- published: 17 Nov 2020
- views: 41477
16:30
5.1 What is a Dynamical System?
- Order: Reorder
- Duration: 16:30
- Uploaded Date: 26 Aug 2018
- views: 30562
Unit 5 Module 1
Algorithmic Information Dynamics: A Computational Approach to Causality and Living Systems---From Networks to Cells
by Hector Zenil and Narsis A...
Unit 5 Module 1
Algorithmic Information Dynamics: A Computational Approach to Causality and Living Systems---From Networks to Cells
by Hector Zenil and Narsis A. Kiani
Algorithmic Dynamics Lab
www.algorithmicdynamics.net
https://wn.com/5.1_What_Is_A_Dynamical_System
Unit 5 Module 1
Algorithmic Information Dynamics: A Computational Approach to Causality and Living Systems---From Networks to Cells
by Hector Zenil and Narsis A. Kiani
Algorithmic Dynamics Lab
www.algorithmicdynamics.net
- published: 26 Aug 2018
- views: 30562
32:11
Topics in Dynamical Systems: Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos
- Order: Reorder
- Duration: 32:11
- Uploaded Date: 16 Jan 2023
- views: 25354
This video provides a high-level overview of dynamical systems, which describe the changing world around us. Topics include nonlinear dynamics, linearization a...
This video provides a high-level overview of dynamical systems, which describe the changing world around us. Topics include nonlinear dynamics, linearization at fixed points, eigenvalues and eigenvectors, bifurcations, invariant manifolds, and chaos!!
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Introduction
4:35 Linearization at a Fixed Point
9:37 Why We Linearize: Eigenvalues and Eigenvectors
14:46 Nonlinear Example: The Duffing Equation
19:59 Stable and Unstable Manifolds
21:12 Bifurcations
25:20 Discrete-Time Dynamics: Population Dynamics
27:02 Integrating Dynamical System Trajectories
29:07 Chaos and Mixing
https://wn.com/Topics_In_Dynamical_Systems_Fixed_Points,_Linearization,_Invariant_Manifolds,_Bifurcations_Chaos
This video provides a high-level overview of dynamical systems, which describe the changing world around us. Topics include nonlinear dynamics, linearization at fixed points, eigenvalues and eigenvectors, bifurcations, invariant manifolds, and chaos!!
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Introduction
4:35 Linearization at a Fixed Point
9:37 Why We Linearize: Eigenvalues and Eigenvectors
14:46 Nonlinear Example: The Duffing Equation
19:59 Stable and Unstable Manifolds
21:12 Bifurcations
25:20 Discrete-Time Dynamics: Population Dynamics
27:02 Integrating Dynamical System Trajectories
29:07 Chaos and Mixing
- published: 16 Jan 2023
- views: 25354
16:36
Introduction to System Dynamics: Overview
- Order: Reorder
- Duration: 16:36
- Uploaded Date: 28 Jul 2014
- views: 363534
MIT 15.871 Introduction to System Dynamics, Fall 2013
View the complete course: http://ocw.mit.edu/15-871F13
Instructor: John Sterman
Professor John Sterman in...
MIT 15.871 Introduction to System Dynamics, Fall 2013
View the complete course: http://ocw.mit.edu/15-871F13
Instructor: John Sterman
Professor John Sterman introduces system dynamics and talks about the course.
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
https://wn.com/Introduction_To_System_Dynamics_Overview
MIT 15.871 Introduction to System Dynamics, Fall 2013
View the complete course: http://ocw.mit.edu/15-871F13
Instructor: John Sterman
Professor John Sterman introduces system dynamics and talks about the course.
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
- published: 28 Jul 2014
- views: 363534
6:41
Dynamical Systems Introduction
- Order: Reorder
- Duration: 6:41
- Uploaded Date: 10 Apr 2015
- views: 76554
Find the complete course at the Si Network Platform → https://tinyurl.com/4n89knfk
Dynamical systems is a area of mathematics and science that studies how the...
Find the complete course at the Si Network Platform → https://tinyurl.com/4n89knfk
Dynamical systems is a area of mathematics and science that studies how the state of systems change over time, in this module we will lay down the foundations to understanding dynamical systems as we talk about phase space and the simplest types of motion, transients and periodic motion, setting us up to approach the topic of nonlinear dynamical systems in the next module.
Within science and mathematics, dynamics is the study of how things change with respect to time, as opposed to describing things simply in terms of their static properties the patterns we observe all around us in how the state of things change overtime is an alternative ways through which we can describe the phenomena we see in our world.
A state space also called phase space is a model used within dynamic systems to capture this change in a system’s state overtime. A state space of a dynamical system is a two or possibly three-dimensional graph in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the state space. Now we can model the change in a system’s state in two ways, as continuous or discrete.
Firstly as continues where the time interval between our measurements is negligibly small making it appear as one long continuum and this is done through the language of calculus. Calculus and differential equations have formed a key part of the language of modern science since the days of Newton and Leibniz. Differential equations are great for few elements they give us lots of information but they also become very complicated very quickly.
On the other hand we can measure time as discrete meaning there is a discernable time interval between each measurement and we use what are called iterative maps to do this. Iterative maps give us less information but are much simpler and better suited to dealing with very many entities, where feedback is important. Where as differential equations are central to modern science iterative maps are central to the study of nonlinear systems and their dynamics as they allow us to take the output to the previous state of the system and feed it back into the next iteration, thus making them well designed to capture the feedback characteristic of nonlinear systems.
The first type of motion we might encounter is simple transient motion, that is to say some system that gravitates towards a stable equilibrium and then stays there, such as putting a ball in a bowl it will role around for a short period before it settles at the point of least potential gravity, its so called equilibrium and then will just stay there until perturbed by some external force.
Next we might see periodic motion, for example the motion of the planets around the sun is periodic. This type of periodic motion is of cause very predictable we can predict far out into the future and way back into the past when eclipses happen. In these systems small disturbances are often rectified and do not increase to alter the systems trajectory very much in the long run. The rising and receding motion of the tides or the change in traffic lights are also example of periodic motion. Whereas in our first type of motion the system simply moves towards its equilibrium point, in this second periodic motion it is more like it is cycling around some equilibrium.
All dynamic systems require some input of energy to drive them, in physics they are referred to as dissipative systems as they are constantly dissipating the energy being inputted to the system in the form of motion or change. A system in this periodic motion is bound to its source of energy and its trajectory follows some periodic motion around it or towards and away from it. In our example of the planet’s orbit, it is following a periodic motion because of the gravitational force the sun exerts on it, if it were not for this driving force, the motion would cease to exist.
Learn about the Systems Innovation Network on our social media:
→ Twitter: http://bit.ly/2JuNmXX
→ LinkedIn: http://bit.ly/2YCP2U6
https://wn.com/Dynamical_Systems_Introduction
Find the complete course at the Si Network Platform → https://tinyurl.com/4n89knfk
Dynamical systems is a area of mathematics and science that studies how the state of systems change over time, in this module we will lay down the foundations to understanding dynamical systems as we talk about phase space and the simplest types of motion, transients and periodic motion, setting us up to approach the topic of nonlinear dynamical systems in the next module.
Within science and mathematics, dynamics is the study of how things change with respect to time, as opposed to describing things simply in terms of their static properties the patterns we observe all around us in how the state of things change overtime is an alternative ways through which we can describe the phenomena we see in our world.
A state space also called phase space is a model used within dynamic systems to capture this change in a system’s state overtime. A state space of a dynamical system is a two or possibly three-dimensional graph in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the state space. Now we can model the change in a system’s state in two ways, as continuous or discrete.
Firstly as continues where the time interval between our measurements is negligibly small making it appear as one long continuum and this is done through the language of calculus. Calculus and differential equations have formed a key part of the language of modern science since the days of Newton and Leibniz. Differential equations are great for few elements they give us lots of information but they also become very complicated very quickly.
On the other hand we can measure time as discrete meaning there is a discernable time interval between each measurement and we use what are called iterative maps to do this. Iterative maps give us less information but are much simpler and better suited to dealing with very many entities, where feedback is important. Where as differential equations are central to modern science iterative maps are central to the study of nonlinear systems and their dynamics as they allow us to take the output to the previous state of the system and feed it back into the next iteration, thus making them well designed to capture the feedback characteristic of nonlinear systems.
The first type of motion we might encounter is simple transient motion, that is to say some system that gravitates towards a stable equilibrium and then stays there, such as putting a ball in a bowl it will role around for a short period before it settles at the point of least potential gravity, its so called equilibrium and then will just stay there until perturbed by some external force.
Next we might see periodic motion, for example the motion of the planets around the sun is periodic. This type of periodic motion is of cause very predictable we can predict far out into the future and way back into the past when eclipses happen. In these systems small disturbances are often rectified and do not increase to alter the systems trajectory very much in the long run. The rising and receding motion of the tides or the change in traffic lights are also example of periodic motion. Whereas in our first type of motion the system simply moves towards its equilibrium point, in this second periodic motion it is more like it is cycling around some equilibrium.
All dynamic systems require some input of energy to drive them, in physics they are referred to as dissipative systems as they are constantly dissipating the energy being inputted to the system in the form of motion or change. A system in this periodic motion is bound to its source of energy and its trajectory follows some periodic motion around it or towards and away from it. In our example of the planet’s orbit, it is following a periodic motion because of the gravitational force the sun exerts on it, if it were not for this driving force, the motion would cease to exist.
Learn about the Systems Innovation Network on our social media:
→ Twitter: http://bit.ly/2JuNmXX
→ LinkedIn: http://bit.ly/2YCP2U6
- published: 10 Apr 2015
- views: 76554
12:37
Chaos Theory: the language of (in)stability
- Order: Reorder
- Duration: 12:37
- Uploaded Date: 18 May 2021
- views: 571910
The field of study of chaos has its roots in differential equations and dynamical systems, the very language that is used to describe how any physical system ev...
The field of study of chaos has its roots in differential equations and dynamical systems, the very language that is used to describe how any physical system evolves in the real world. This video aims to tell the story of chaos step by step, from simple non-chaotic systems, to different types of attractors, to fractal spaces and the language of unpredictability.
Timestamps:
00:00 - Intro
02:17 - Dynamical Systems
04:11 - Attractors
06:28 - Lorenz Attractor: Strange
08:54 - Lorenz Attractor: Chaotic
Music by:
Karl Casey @ White Bat Audio
https://www.youtube.com/watch?v=Gao-DHIyj0Q&ab_channel=WhiteBatAudio
https://www.youtube.com/watch?v=2gsn1HrDtdI&ab_channel=WhiteBatAudio
https://www.youtube.com/channel/UC_6hQy4elsyHhCOskZo0U5g
LAKEY INSPIRED
https://soundcloud.com/lakeyinspired
https://www.youtube.com/channel/UCOmy8wuTpC95lefU5d1dt2Q
Phil Lober
https://www.youtube.com/@MusicOfPhil
https://www.youtube.com/watch?v=vj_tauJsURI&ab_channel=PhilLober
References
Chaos: The Mathematics Behind the Butterfly Effect - James Manning
https://www.colby.edu/mathstats/wp-content/uploads/sites/81/2017/08/2017-Manning-Thesis.pdf
YFX1520 Nonlinear Dynamics Lecture 9 - Dmitri Kartofelev
https://www.ioc.ee/~dima/YFX1520/LectureNotes_9.pdf
Attractors: Nonstrange to Chaotic - Robert L. V. Taylor
http://evoq-eval.siam.org/Portals/0/Publications/SIURO/Vol4/Attractors_Nonstrange_to_Chaotic.pdf?ver=2018-04-06-103239-977
https://wn.com/Chaos_Theory_The_Language_Of_(In)Stability
The field of study of chaos has its roots in differential equations and dynamical systems, the very language that is used to describe how any physical system evolves in the real world. This video aims to tell the story of chaos step by step, from simple non-chaotic systems, to different types of attractors, to fractal spaces and the language of unpredictability.
Timestamps:
00:00 - Intro
02:17 - Dynamical Systems
04:11 - Attractors
06:28 - Lorenz Attractor: Strange
08:54 - Lorenz Attractor: Chaotic
Music by:
Karl Casey @ White Bat Audio
https://www.youtube.com/watch?v=Gao-DHIyj0Q&ab_channel=WhiteBatAudio
https://www.youtube.com/watch?v=2gsn1HrDtdI&ab_channel=WhiteBatAudio
https://www.youtube.com/channel/UC_6hQy4elsyHhCOskZo0U5g
LAKEY INSPIRED
https://soundcloud.com/lakeyinspired
https://www.youtube.com/channel/UCOmy8wuTpC95lefU5d1dt2Q
Phil Lober
https://www.youtube.com/@MusicOfPhil
https://www.youtube.com/watch?v=vj_tauJsURI&ab_channel=PhilLober
References
Chaos: The Mathematics Behind the Butterfly Effect - James Manning
https://www.colby.edu/mathstats/wp-content/uploads/sites/81/2017/08/2017-Manning-Thesis.pdf
YFX1520 Nonlinear Dynamics Lecture 9 - Dmitri Kartofelev
https://www.ioc.ee/~dima/YFX1520/LectureNotes_9.pdf
Attractors: Nonstrange to Chaotic - Robert L. V. Taylor
http://evoq-eval.siam.org/Portals/0/Publications/SIURO/Vol4/Attractors_Nonstrange_to_Chaotic.pdf?ver=2018-04-06-103239-977
- published: 18 May 2021
- views: 571910
12:51
Chaos: The Science of the Butterfly Effect
- Order: Reorder
- Duration: 12:51
- Uploaded Date: 06 Dec 2019
- views: 7204626
Chaos theory means deterministic systems can be unpredictable. Thanks to LastPass for sponsoring this video. Click here to start using LastPass: https://ve42.co...
Chaos theory means deterministic systems can be unpredictable. Thanks to LastPass for sponsoring this video. Click here to start using LastPass: https://ve42.co/VeLP
Animations by Prof. Robert Ghrist: https://ve42.co/Ghrist
Want to know more about chaos theory and non-linear dynamical systems? Check out: https://ve42.co/chaos-math
Butterfly footage courtesy of Phil Torres and The Jungle Diaries: https://ve42.co/monarch
Solar system, 3-body and printout animations by Jonny Hyman
Some animations made with Universe Sandbox: https://universesandbox.com/
Special thanks to Prof. Mason Porter at UCLA who I interviewed for this video.
I have long wanted to make a video about chaos, ever since reading James Gleick's fantastic book, Chaos. I hope this video gives an idea of phase space - a picture of dynamical systems in which each point completely represents the state of the system. For a pendulum, phase space is only 2-dimensional and you can get orbits (in the case of an undamped pendulum) or an inward spiral (in the case of a pendulum with friction). For the Lorenz equations we need three dimensions to show the phase space. The attractor you find for these equations is said to be strange and chaotic because there is no loop, only infinite curves that never intersect. This explains why the motion is so unpredictable - two different initial conditions that are very close together can end up arbitrarily far apart.
Music from https://epidemicsound.com "The Longest Rest" "A Sound Foundation" "Seaweed"
https://wn.com/Chaos_The_Science_Of_The_Butterfly_Effect
Chaos theory means deterministic systems can be unpredictable. Thanks to LastPass for sponsoring this video. Click here to start using LastPass: https://ve42.co/VeLP
Animations by Prof. Robert Ghrist: https://ve42.co/Ghrist
Want to know more about chaos theory and non-linear dynamical systems? Check out: https://ve42.co/chaos-math
Butterfly footage courtesy of Phil Torres and The Jungle Diaries: https://ve42.co/monarch
Solar system, 3-body and printout animations by Jonny Hyman
Some animations made with Universe Sandbox: https://universesandbox.com/
Special thanks to Prof. Mason Porter at UCLA who I interviewed for this video.
I have long wanted to make a video about chaos, ever since reading James Gleick's fantastic book, Chaos. I hope this video gives an idea of phase space - a picture of dynamical systems in which each point completely represents the state of the system. For a pendulum, phase space is only 2-dimensional and you can get orbits (in the case of an undamped pendulum) or an inward spiral (in the case of a pendulum with friction). For the Lorenz equations we need three dimensions to show the phase space. The attractor you find for these equations is said to be strange and chaotic because there is no loop, only infinite curves that never intersect. This explains why the motion is so unpredictable - two different initial conditions that are very close together can end up arbitrarily far apart.
Music from https://epidemicsound.com "The Longest Rest" "A Sound Foundation" "Seaweed"
- published: 06 Dec 2019
- views: 7204626
57:49
WG Virtual Seminars, Hypothalamic-Pituitary-Adrenal Axis Dynamics, Vukojevic, October 17, 2024
- Order: Reorder
- Duration: 57:49
- Uploaded Date: 18 Oct 2024
- views: 32
Quenching Small-Amplitude Limit Cycle Oscillations for Predictive Modeling of Complex Molecular Mechanisms Underlying Chemical and Biochemical Oscillatory React...
Quenching Small-Amplitude Limit Cycle Oscillations for Predictive Modeling of Complex Molecular Mechanisms Underlying Chemical and Biochemical Oscillatory Reactions. Insights into the Effects of Ethanol on Hypothalamic-Pituitary-Adrenal (HPA) Axis Dynamics
Vladana Vukojevic, PhD
Karolinska Institute
Quenching Small-Amplitude Limit Cycle Oscillations, i.e., Quenching Analysis (QA), is a method specifically designed to take the advantage of the oscillatory dynamics that emerges in the vicinity of a supercritical Hopf bifurcation and harvest it to acquire unique quantitative information about the investigated system that can easily be compared with model predictions. To this aim, QA relies on a series of controlled additions of a compound that is inherent to the system or reacts with a reactive species in the system, to immediately, yet temporarily suppress the oscillations. For each species, QA yields two values, the quenching concentration (qi), i.e., the amount of species i needed, and the quenching phase (ji), i.e., the phase angle with respect to a reference point in an oscillation, at which this amount is to be added to temporarily pause the oscillations. By comparing the experimentally derived quenching concentrations and quenching phases with results obtained from mechanistic models, one can determine whether key reaction pathways are correctly identified and incorporated in the model of the reaction mechanism and assess how realistically the model reflects the true mechanism of the investigated system. The aim of this presentation is twofold: to present the theoretical background behind QA and to demonstrate the potential of this method for understanding specific features of a complex neuroendocrine dynamical system, the Hypothalamic-Pituitary-Adrenal (HPA) axis, under normal physiology and response to ethanol-induced stress.
For more information see:
https://ki.se/en/people/vladana-vukojevic
and
1) Čupić Ž, Stanojević A, Marković VM, Kolar-Anić L, Terenius L, Vukojević V. The HPA axis and ethanol: a synthesis of mathematical modelling and experimental observations. Addict. Biol. 2017 22(6):1486-1500. doi: 10.1111/adb.12409
2) Abulseoud OA, Ho MC, Choi D-S, Stanojević A, Čupić Ž, Kolar-Anić Lj, Vukojević V. Corticosterone oscillations during mania induction in the lateral hypothalamic kindled rat experimental observations and mathematical modelling. PLoS One 2017, 12(5):e0177551. doi: 10.1371/journal.pone.0177551
3) Stanojević A, Marković VM, Čupić Ž, Kolar-Anić Lj, Vukojević V. Advances in mathematical modelling of the hypothalamic–pituitary–adrenal (HPA) axis dynamics and the neuroendocrine response to stress. Current Opinion in Chemical Engineering 2018, 21:84–95. doi:10.1016/j.coche.2018.04.003
*Contents*
00:00 - Introduction
09:12 - Predictive Modeling of Molecular Mechanisms of the Effects of Ethanol on Hypothalamic-Pituitary-Adrenal Axis Dynamics
51:10 - Questions and Discussions
If you found this video useful, please check out our other videos on computational modeling, infection and immunology: https://youtube.com/playlist?list=PLiEtieOeWbMKh9VcQoinSwODcSZKMTGat
Please consider joining our IMAG/MSM WG on Multiscale Modeling and Viral Pandemics: https://www.imagwiki.nibib.nih.gov/content/msm-viral-pandemics-meetings
Please also consider joining the Global Alliance for Immune Prediction and Intervention: http://glimprint.org/
https://wn.com/Wg_Virtual_Seminars,_Hypothalamic_Pituitary_Adrenal_Axis_Dynamics,_Vukojevic,_October_17,_2024
Quenching Small-Amplitude Limit Cycle Oscillations for Predictive Modeling of Complex Molecular Mechanisms Underlying Chemical and Biochemical Oscillatory Reactions. Insights into the Effects of Ethanol on Hypothalamic-Pituitary-Adrenal (HPA) Axis Dynamics
Vladana Vukojevic, PhD
Karolinska Institute
Quenching Small-Amplitude Limit Cycle Oscillations, i.e., Quenching Analysis (QA), is a method specifically designed to take the advantage of the oscillatory dynamics that emerges in the vicinity of a supercritical Hopf bifurcation and harvest it to acquire unique quantitative information about the investigated system that can easily be compared with model predictions. To this aim, QA relies on a series of controlled additions of a compound that is inherent to the system or reacts with a reactive species in the system, to immediately, yet temporarily suppress the oscillations. For each species, QA yields two values, the quenching concentration (qi), i.e., the amount of species i needed, and the quenching phase (ji), i.e., the phase angle with respect to a reference point in an oscillation, at which this amount is to be added to temporarily pause the oscillations. By comparing the experimentally derived quenching concentrations and quenching phases with results obtained from mechanistic models, one can determine whether key reaction pathways are correctly identified and incorporated in the model of the reaction mechanism and assess how realistically the model reflects the true mechanism of the investigated system. The aim of this presentation is twofold: to present the theoretical background behind QA and to demonstrate the potential of this method for understanding specific features of a complex neuroendocrine dynamical system, the Hypothalamic-Pituitary-Adrenal (HPA) axis, under normal physiology and response to ethanol-induced stress.
For more information see:
https://ki.se/en/people/vladana-vukojevic
and
1) Čupić Ž, Stanojević A, Marković VM, Kolar-Anić L, Terenius L, Vukojević V. The HPA axis and ethanol: a synthesis of mathematical modelling and experimental observations. Addict. Biol. 2017 22(6):1486-1500. doi: 10.1111/adb.12409
2) Abulseoud OA, Ho MC, Choi D-S, Stanojević A, Čupić Ž, Kolar-Anić Lj, Vukojević V. Corticosterone oscillations during mania induction in the lateral hypothalamic kindled rat experimental observations and mathematical modelling. PLoS One 2017, 12(5):e0177551. doi: 10.1371/journal.pone.0177551
3) Stanojević A, Marković VM, Čupić Ž, Kolar-Anić Lj, Vukojević V. Advances in mathematical modelling of the hypothalamic–pituitary–adrenal (HPA) axis dynamics and the neuroendocrine response to stress. Current Opinion in Chemical Engineering 2018, 21:84–95. doi:10.1016/j.coche.2018.04.003
*Contents*
00:00 - Introduction
09:12 - Predictive Modeling of Molecular Mechanisms of the Effects of Ethanol on Hypothalamic-Pituitary-Adrenal Axis Dynamics
51:10 - Questions and Discussions
If you found this video useful, please check out our other videos on computational modeling, infection and immunology: https://youtube.com/playlist?list=PLiEtieOeWbMKh9VcQoinSwODcSZKMTGat
Please consider joining our IMAG/MSM WG on Multiscale Modeling and Viral Pandemics: https://www.imagwiki.nibib.nih.gov/content/msm-viral-pandemics-meetings
Please also consider joining the Global Alliance for Immune Prediction and Intervention: http://glimprint.org/
- published: 18 Oct 2024
- views: 32
17:43
Dynamical Systems Theory - Motor Control and Learning
- Order: Reorder
- Duration: 17:43
- Uploaded Date: 21 Jul 2022
- views: 14364
Dynamical Systems Theory - Motor Control and Learning: Dynamical systems theory, Dynamical pattern theory, Coordination dynamics theory, Ecological theory, Acti...
Dynamical Systems Theory - Motor Control and Learning: Dynamical systems theory, Dynamical pattern theory, Coordination dynamics theory, Ecological theory, Action theory, Multidisciplinary perspective, Physics, Biology, Chemistry, Mathematics, Human movement control, Nonlinear dynamics, Boiling water, Variable, Nonlinear behavioral change, Human coordinated movement, Coordination patterns, Speed, Dynamics, Stability, Attractors, Attractor state, Energy-efficient, Walking gait, Running gait, Speed of locomotion, Order parameters, Collective variables, Relative phase, Rhythmic movement, In-phase, Antiphase, Control parameter, Self-organization, Hurricanes, Coordinative structures, Ensemble of muscles and joints, Muscle synergies, Motor synergies, Intrinsic coordinative structures, Developed through practice, Symmetrical, Asymmetrical, Perception-action coupling, Spatial coordination, Temporal coordination, Tau, Time to contact
Medical Disclaimer: The videos posted on this channel are for educational purposes only and should not be construed as medical advice. Nothing posted on this channel is medical advice or a substitute for advice from your physician or healthcare provider. Always contact your physician or healthcare provider with any questions about a medical condition or your personal health.
References
Kandel, E. R., Schwartz, J. H., & Jessell, T. M. (2000). Principles of neural science, (4th ed.). New York City, New York: McGraw-Hill Health Professions Division.
Magill, R., & Anderson, D. (2021). Motor learning and control: Concepts and applications, (12th ed.). New York City, New York: McGraww Hill, LLC.
Martin, J. H. (2003). Neuroanatomy text and atlas, (3rd ed.). New York City, NY: McGraw Hill Companies, Inc.
Rosenbaum, D. A. (2010). Human motor control, (2nd ed.). Burlington, MA: Elsevier Inc.
https://wn.com/Dynamical_Systems_Theory_Motor_Control_And_Learning
Dynamical Systems Theory - Motor Control and Learning: Dynamical systems theory, Dynamical pattern theory, Coordination dynamics theory, Ecological theory, Action theory, Multidisciplinary perspective, Physics, Biology, Chemistry, Mathematics, Human movement control, Nonlinear dynamics, Boiling water, Variable, Nonlinear behavioral change, Human coordinated movement, Coordination patterns, Speed, Dynamics, Stability, Attractors, Attractor state, Energy-efficient, Walking gait, Running gait, Speed of locomotion, Order parameters, Collective variables, Relative phase, Rhythmic movement, In-phase, Antiphase, Control parameter, Self-organization, Hurricanes, Coordinative structures, Ensemble of muscles and joints, Muscle synergies, Motor synergies, Intrinsic coordinative structures, Developed through practice, Symmetrical, Asymmetrical, Perception-action coupling, Spatial coordination, Temporal coordination, Tau, Time to contact
Medical Disclaimer: The videos posted on this channel are for educational purposes only and should not be construed as medical advice. Nothing posted on this channel is medical advice or a substitute for advice from your physician or healthcare provider. Always contact your physician or healthcare provider with any questions about a medical condition or your personal health.
References
Kandel, E. R., Schwartz, J. H., & Jessell, T. M. (2000). Principles of neural science, (4th ed.). New York City, New York: McGraw-Hill Health Professions Division.
Magill, R., & Anderson, D. (2021). Motor learning and control: Concepts and applications, (12th ed.). New York City, New York: McGraww Hill, LLC.
Martin, J. H. (2003). Neuroanatomy text and atlas, (3rd ed.). New York City, NY: McGraw Hill Companies, Inc.
Rosenbaum, D. A. (2010). Human motor control, (2nd ed.). Burlington, MA: Elsevier Inc.
- published: 21 Jul 2022
- views: 14364
17:53
The Anatomy of a Dynamical System
Dynamical systems are how we model the changing world around us.
This video explores the...
published: 30 Jul 2021
The Anatomy of a Dynamical System
The Anatomy of a Dynamical System
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- published: 30 Jul 2021
- views: 86699
Dynamical systems are how we model the changing world around us.
This video explores the components that make up a dynamical system.
Follow updates on Twitter @eigensteve
website: eigensteve.com
This video was produced at the University of Washington
2:10
Inside Dynamical Systems and the Mathematics of Change
Bryna Kra searches for structures using symbolic dynamics. “[I love] finding order where y...
published: 17 Nov 2020
Inside Dynamical Systems and the Mathematics of Change
Inside Dynamical Systems and the Mathematics of Change
- Report rights infringement
- published: 17 Nov 2020
- views: 41477
Bryna Kra searches for structures using symbolic dynamics. “[I love] finding order where you didn’t know it existed,” she said. "This is how I think about math: It’s about how things fit together." Read the full story at Quanta Magazine: https://www.quantamagazine.org/bryna-kra-searches-symbols-for-the-rules-of-change-20201117/
16:30
5.1 What is a Dynamical System?
Unit 5 Module 1
Algorithmic Information Dynamics: A Computational Approach to Causality an...
published: 26 Aug 2018
5.1 What is a Dynamical System?
5.1 What is a Dynamical System?
- Report rights infringement
- published: 26 Aug 2018
- views: 30562
Unit 5 Module 1
Algorithmic Information Dynamics: A Computational Approach to Causality and Living Systems---From Networks to Cells
by Hector Zenil and Narsis A. Kiani
Algorithmic Dynamics Lab
www.algorithmicdynamics.net
32:11
Topics in Dynamical Systems: Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos
This video provides a high-level overview of dynamical systems, which describe the changin...
published: 16 Jan 2023
Topics in Dynamical Systems: Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos
Topics in Dynamical Systems: Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos
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- published: 16 Jan 2023
- views: 25354
This video provides a high-level overview of dynamical systems, which describe the changing world around us. Topics include nonlinear dynamics, linearization at fixed points, eigenvalues and eigenvectors, bifurcations, invariant manifolds, and chaos!!
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Introduction
4:35 Linearization at a Fixed Point
9:37 Why We Linearize: Eigenvalues and Eigenvectors
14:46 Nonlinear Example: The Duffing Equation
19:59 Stable and Unstable Manifolds
21:12 Bifurcations
25:20 Discrete-Time Dynamics: Population Dynamics
27:02 Integrating Dynamical System Trajectories
29:07 Chaos and Mixing
16:36
Introduction to System Dynamics: Overview
MIT 15.871 Introduction to System Dynamics, Fall 2013
View the complete course: http://ocw...
published: 28 Jul 2014
Introduction to System Dynamics: Overview
Introduction to System Dynamics: Overview
- Report rights infringement
- published: 28 Jul 2014
- views: 363534
MIT 15.871 Introduction to System Dynamics, Fall 2013
View the complete course: http://ocw.mit.edu/15-871F13
Instructor: John Sterman
Professor John Sterman introduces system dynamics and talks about the course.
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu
6:41
Dynamical Systems Introduction
Find the complete course at the Si Network Platform → https://tinyurl.com/4n89knfk
Dynam...
published: 10 Apr 2015
Dynamical Systems Introduction
Dynamical Systems Introduction
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- published: 10 Apr 2015
- views: 76554
Find the complete course at the Si Network Platform → https://tinyurl.com/4n89knfk
Dynamical systems is a area of mathematics and science that studies how the state of systems change over time, in this module we will lay down the foundations to understanding dynamical systems as we talk about phase space and the simplest types of motion, transients and periodic motion, setting us up to approach the topic of nonlinear dynamical systems in the next module.
Within science and mathematics, dynamics is the study of how things change with respect to time, as opposed to describing things simply in terms of their static properties the patterns we observe all around us in how the state of things change overtime is an alternative ways through which we can describe the phenomena we see in our world.
A state space also called phase space is a model used within dynamic systems to capture this change in a system’s state overtime. A state space of a dynamical system is a two or possibly three-dimensional graph in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the state space. Now we can model the change in a system’s state in two ways, as continuous or discrete.
Firstly as continues where the time interval between our measurements is negligibly small making it appear as one long continuum and this is done through the language of calculus. Calculus and differential equations have formed a key part of the language of modern science since the days of Newton and Leibniz. Differential equations are great for few elements they give us lots of information but they also become very complicated very quickly.
On the other hand we can measure time as discrete meaning there is a discernable time interval between each measurement and we use what are called iterative maps to do this. Iterative maps give us less information but are much simpler and better suited to dealing with very many entities, where feedback is important. Where as differential equations are central to modern science iterative maps are central to the study of nonlinear systems and their dynamics as they allow us to take the output to the previous state of the system and feed it back into the next iteration, thus making them well designed to capture the feedback characteristic of nonlinear systems.
The first type of motion we might encounter is simple transient motion, that is to say some system that gravitates towards a stable equilibrium and then stays there, such as putting a ball in a bowl it will role around for a short period before it settles at the point of least potential gravity, its so called equilibrium and then will just stay there until perturbed by some external force.
Next we might see periodic motion, for example the motion of the planets around the sun is periodic. This type of periodic motion is of cause very predictable we can predict far out into the future and way back into the past when eclipses happen. In these systems small disturbances are often rectified and do not increase to alter the systems trajectory very much in the long run. The rising and receding motion of the tides or the change in traffic lights are also example of periodic motion. Whereas in our first type of motion the system simply moves towards its equilibrium point, in this second periodic motion it is more like it is cycling around some equilibrium.
All dynamic systems require some input of energy to drive them, in physics they are referred to as dissipative systems as they are constantly dissipating the energy being inputted to the system in the form of motion or change. A system in this periodic motion is bound to its source of energy and its trajectory follows some periodic motion around it or towards and away from it. In our example of the planet’s orbit, it is following a periodic motion because of the gravitational force the sun exerts on it, if it were not for this driving force, the motion would cease to exist.
Learn about the Systems Innovation Network on our social media:
→ Twitter: http://bit.ly/2JuNmXX
→ LinkedIn: http://bit.ly/2YCP2U6
12:37
Chaos Theory: the language of (in)stability
The field of study of chaos has its roots in differential equations and dynamical systems,...
published: 18 May 2021
Chaos Theory: the language of (in)stability
Chaos Theory: the language of (in)stability
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- published: 18 May 2021
- views: 571910
The field of study of chaos has its roots in differential equations and dynamical systems, the very language that is used to describe how any physical system evolves in the real world. This video aims to tell the story of chaos step by step, from simple non-chaotic systems, to different types of attractors, to fractal spaces and the language of unpredictability.
Timestamps:
00:00 - Intro
02:17 - Dynamical Systems
04:11 - Attractors
06:28 - Lorenz Attractor: Strange
08:54 - Lorenz Attractor: Chaotic
Music by:
Karl Casey @ White Bat Audio
https://www.youtube.com/watch?v=Gao-DHIyj0Q&ab_channel=WhiteBatAudio
https://www.youtube.com/watch?v=2gsn1HrDtdI&ab_channel=WhiteBatAudio
https://www.youtube.com/channel/UC_6hQy4elsyHhCOskZo0U5g
LAKEY INSPIRED
https://soundcloud.com/lakeyinspired
https://www.youtube.com/channel/UCOmy8wuTpC95lefU5d1dt2Q
Phil Lober
https://www.youtube.com/@MusicOfPhil
https://www.youtube.com/watch?v=vj_tauJsURI&ab_channel=PhilLober
References
Chaos: The Mathematics Behind the Butterfly Effect - James Manning
https://www.colby.edu/mathstats/wp-content/uploads/sites/81/2017/08/2017-Manning-Thesis.pdf
YFX1520 Nonlinear Dynamics Lecture 9 - Dmitri Kartofelev
https://www.ioc.ee/~dima/YFX1520/LectureNotes_9.pdf
Attractors: Nonstrange to Chaotic - Robert L. V. Taylor
http://evoq-eval.siam.org/Portals/0/Publications/SIURO/Vol4/Attractors_Nonstrange_to_Chaotic.pdf?ver=2018-04-06-103239-977
12:51
Chaos: The Science of the Butterfly Effect
Chaos theory means deterministic systems can be unpredictable. Thanks to LastPass for spon...
published: 06 Dec 2019
Chaos: The Science of the Butterfly Effect
Chaos: The Science of the Butterfly Effect
- Report rights infringement
- published: 06 Dec 2019
- views: 7204626
Chaos theory means deterministic systems can be unpredictable. Thanks to LastPass for sponsoring this video. Click here to start using LastPass: https://ve42.co/VeLP
Animations by Prof. Robert Ghrist: https://ve42.co/Ghrist
Want to know more about chaos theory and non-linear dynamical systems? Check out: https://ve42.co/chaos-math
Butterfly footage courtesy of Phil Torres and The Jungle Diaries: https://ve42.co/monarch
Solar system, 3-body and printout animations by Jonny Hyman
Some animations made with Universe Sandbox: https://universesandbox.com/
Special thanks to Prof. Mason Porter at UCLA who I interviewed for this video.
I have long wanted to make a video about chaos, ever since reading James Gleick's fantastic book, Chaos. I hope this video gives an idea of phase space - a picture of dynamical systems in which each point completely represents the state of the system. For a pendulum, phase space is only 2-dimensional and you can get orbits (in the case of an undamped pendulum) or an inward spiral (in the case of a pendulum with friction). For the Lorenz equations we need three dimensions to show the phase space. The attractor you find for these equations is said to be strange and chaotic because there is no loop, only infinite curves that never intersect. This explains why the motion is so unpredictable - two different initial conditions that are very close together can end up arbitrarily far apart.
Music from https://epidemicsound.com "The Longest Rest" "A Sound Foundation" "Seaweed"
57:49
WG Virtual Seminars, Hypothalamic-Pituitary-Adrenal Axis Dynamics, Vukojevic, October 17, 2024
Quenching Small-Amplitude Limit Cycle Oscillations for Predictive Modeling of Complex Mole...
published: 18 Oct 2024
WG Virtual Seminars, Hypothalamic-Pituitary-Adrenal Axis Dynamics, Vukojevic, October 17, 2024
WG Virtual Seminars, Hypothalamic-Pituitary-Adrenal Axis Dynamics, Vukojevic, October 17, 2024
- Report rights infringement
- published: 18 Oct 2024
- views: 32
Quenching Small-Amplitude Limit Cycle Oscillations for Predictive Modeling of Complex Molecular Mechanisms Underlying Chemical and Biochemical Oscillatory Reactions. Insights into the Effects of Ethanol on Hypothalamic-Pituitary-Adrenal (HPA) Axis Dynamics
Vladana Vukojevic, PhD
Karolinska Institute
Quenching Small-Amplitude Limit Cycle Oscillations, i.e., Quenching Analysis (QA), is a method specifically designed to take the advantage of the oscillatory dynamics that emerges in the vicinity of a supercritical Hopf bifurcation and harvest it to acquire unique quantitative information about the investigated system that can easily be compared with model predictions. To this aim, QA relies on a series of controlled additions of a compound that is inherent to the system or reacts with a reactive species in the system, to immediately, yet temporarily suppress the oscillations. For each species, QA yields two values, the quenching concentration (qi), i.e., the amount of species i needed, and the quenching phase (ji), i.e., the phase angle with respect to a reference point in an oscillation, at which this amount is to be added to temporarily pause the oscillations. By comparing the experimentally derived quenching concentrations and quenching phases with results obtained from mechanistic models, one can determine whether key reaction pathways are correctly identified and incorporated in the model of the reaction mechanism and assess how realistically the model reflects the true mechanism of the investigated system. The aim of this presentation is twofold: to present the theoretical background behind QA and to demonstrate the potential of this method for understanding specific features of a complex neuroendocrine dynamical system, the Hypothalamic-Pituitary-Adrenal (HPA) axis, under normal physiology and response to ethanol-induced stress.
For more information see:
https://ki.se/en/people/vladana-vukojevic
and
1) Čupić Ž, Stanojević A, Marković VM, Kolar-Anić L, Terenius L, Vukojević V. The HPA axis and ethanol: a synthesis of mathematical modelling and experimental observations. Addict. Biol. 2017 22(6):1486-1500. doi: 10.1111/adb.12409
2) Abulseoud OA, Ho MC, Choi D-S, Stanojević A, Čupić Ž, Kolar-Anić Lj, Vukojević V. Corticosterone oscillations during mania induction in the lateral hypothalamic kindled rat experimental observations and mathematical modelling. PLoS One 2017, 12(5):e0177551. doi: 10.1371/journal.pone.0177551
3) Stanojević A, Marković VM, Čupić Ž, Kolar-Anić Lj, Vukojević V. Advances in mathematical modelling of the hypothalamic–pituitary–adrenal (HPA) axis dynamics and the neuroendocrine response to stress. Current Opinion in Chemical Engineering 2018, 21:84–95. doi:10.1016/j.coche.2018.04.003
*Contents*
00:00 - Introduction
09:12 - Predictive Modeling of Molecular Mechanisms of the Effects of Ethanol on Hypothalamic-Pituitary-Adrenal Axis Dynamics
51:10 - Questions and Discussions
If you found this video useful, please check out our other videos on computational modeling, infection and immunology: https://youtube.com/playlist?list=PLiEtieOeWbMKh9VcQoinSwODcSZKMTGat
Please consider joining our IMAG/MSM WG on Multiscale Modeling and Viral Pandemics: https://www.imagwiki.nibib.nih.gov/content/msm-viral-pandemics-meetings
Please also consider joining the Global Alliance for Immune Prediction and Intervention: http://glimprint.org/
17:43
Dynamical Systems Theory - Motor Control and Learning
Dynamical Systems Theory - Motor Control and Learning: Dynamical systems theory, Dynamical...
published: 21 Jul 2022
Dynamical Systems Theory - Motor Control and Learning
Dynamical Systems Theory - Motor Control and Learning
- Report rights infringement
- published: 21 Jul 2022
- views: 14364
Dynamical Systems Theory - Motor Control and Learning: Dynamical systems theory, Dynamical pattern theory, Coordination dynamics theory, Ecological theory, Action theory, Multidisciplinary perspective, Physics, Biology, Chemistry, Mathematics, Human movement control, Nonlinear dynamics, Boiling water, Variable, Nonlinear behavioral change, Human coordinated movement, Coordination patterns, Speed, Dynamics, Stability, Attractors, Attractor state, Energy-efficient, Walking gait, Running gait, Speed of locomotion, Order parameters, Collective variables, Relative phase, Rhythmic movement, In-phase, Antiphase, Control parameter, Self-organization, Hurricanes, Coordinative structures, Ensemble of muscles and joints, Muscle synergies, Motor synergies, Intrinsic coordinative structures, Developed through practice, Symmetrical, Asymmetrical, Perception-action coupling, Spatial coordination, Temporal coordination, Tau, Time to contact
Medical Disclaimer: The videos posted on this channel are for educational purposes only and should not be construed as medical advice. Nothing posted on this channel is medical advice or a substitute for advice from your physician or healthcare provider. Always contact your physician or healthcare provider with any questions about a medical condition or your personal health.
References
Kandel, E. R., Schwartz, J. H., & Jessell, T. M. (2000). Principles of neural science, (4th ed.). New York City, New York: McGraw-Hill Health Professions Division.
Magill, R., & Anderson, D. (2021). Motor learning and control: Concepts and applications, (12th ed.). New York City, New York: McGraww Hill, LLC.
Martin, J. H. (2003). Neuroanatomy text and atlas, (3rd ed.). New York City, NY: McGraw Hill Companies, Inc.
Rosenbaum, D. A. (2010). Human motor control, (2nd ed.). Burlington, MA: Elsevier Inc.
Dynamical system (definition)
The dynamical system concept is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space. The concept unifies very different types of such "rules" in mathematics: the different choices made for how time is measured and the special properties of the ambient space may give an idea of the vastness of the class of objects described by this concept. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the ambient space may be simply a set, without the need of a smooth space-time structure defined on it.
Formal definition
There are two classes of definitions for a dynamical system: one is motivated by ordinary differential equations and is geometrical in flavor; and the other is motivated by ergodic theory and is measure theoretical in flavor. The measure theoretical definitions assume the existence of a measure-preserving transformation. This appears to exclude dissipative systems, as in a dissipative system a small region of phase space shrinks under time evolution. A simple construction (sometimes called the Krylov-Bogolyubov theorem) shows that it is always possible to construct a measure so as to make the evolution rule of the dynamical system a measure-preserving transformation. In the construction a given measure of the state space is summed for all future points of a trajectory, assuring the invariance.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Dynamical_system_(definition)
The Anatomy of a Dynamical System...
Inside Dynamical Systems and the Mathematics of Ch...
5.1 What is a Dynamical System?...
Topics in Dynamical Systems: Fixed Points, Lineari...
Introduction to System Dynamics: Overview...
Dynamical Systems Introduction...
Chaos Theory: the language of (in)stability...
Chaos: The Science of the Butterfly Effect...
WG Virtual Seminars, Hypothalamic-Pituitary-Adrena...