Search results
Results From The WOW.Com Content Network
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...
A discrete dynamical system, discrete-time dynamical system is a tuple (T, M, Φ), where M is a manifold locally diffeomorphic to a Banach space, and Φ is a function. When T is taken to be the integers, it is a cascade or a map. If T is restricted to the non-negative integers we call the system a semi-cascade. [14]
The ergodic theory of dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field of arithmetic combinatorics. Also dynamical systems theory is heavily involved in the relatively recent field of combinatorics on words. Also combinatorial aspects of dynamical systems are studied.
J. de Vries, Topological Dynamical Systems: An Introduction to the Dynamics of Continuous Mappings, De Gruyter Studies in Mathematics, 59, De Gruyter, Berlin, 2014, ISBN 978-3-1103-4073-0 Jian Li and Xiang Dong Ye, Recent development of chaos theory in topological dynamics , Acta Mathematica Sinica, English Series, 2016, Volume 32, Issue 1, pp ...
Linear dynamical systems can be solved exactly, in contrast to most nonlinear ones. Occasionally, a nonlinear system can be solved exactly by a change of variables to a linear system. Moreover, the solutions of (almost) any nonlinear system can be well-approximated by an equivalent linear system near its fixed points. Hence, understanding ...
Dynamical neuroscience describes the non-linear dynamics at many levels of the brain from single neural cells [3] to cognitive processes, sleep states and the behavior of neurons in large-scale neuronal simulation. [4] Neurons have been modeled as nonlinear systems for decades, but dynamical systems are not constrained to neurons. Dynamical ...
Nonlinear Dynamical Systems and Control, a Lyapunov-based approach. Princeton University Press. ISBN 9780691133294. Teschl, G. (2012). Ordinary Differential Equations and Dynamical Systems. Providence: American Mathematical Society. ISBN 978-0-8218-8328-0. Wiggins, S. (2003). Introduction to Applied Nonlinear Dynamical Systems and Chaos (2 ed.).
Complex dynamic systems theory in the field of linguistics is a perspective and approach to the study of second, third and additional language acquisition. The general term complex dynamic systems theory was recommended by Kees de Bot to refer to both complexity theory and dynamic systems theory .