Dynamical systems theory | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-25

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Dynamical_systems_theory


00:01:31 1 Overview
00:02:57 2 History
00:03:40 3 Concepts
00:03:49 3.1 Dynamical systems
00:04:54 3.2 Dynamicism
00:05:23 3.3 Nonlinear system
00:06:07 4 Related fields
00:06:16 4.1 Arithmetic dynamics
00:06:53 4.2 Chaos theory
00:07:39 4.3 Complex systems
00:08:49 4.4 Control theory
00:09:07 4.5 Ergodic theory
00:09:28 4.6 Functional analysis
00:10:14 4.7 Graph dynamical systems
00:10:45 4.8 Projected dynamical systems
00:11:20 4.9 Symbolic dynamics
00:11:46 4.10 System dynamics
00:12:21 4.11 Topological dynamics
00:12:43 5 Applications
00:12:52 5.1 In biomechanics
00:13:47 5.2 In cognitive science
00:15:24 5.3 In second language development
00:16:06 6 See also
00:16:19 7 Notes
00:16:28 8 Further reading
00:18:50 9 External links



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SUMMARY
=======
Dynamical systems theory is an area of mathematics used to describe the behavior of the  complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. 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 field of study is also called just dynamical systems, mathematical dynamical systems theory or the mathematical theory of dynamical systems.