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Dynamical Systems Theory [PDF]
The International Journal of Communication and Linguistic Studies, 2019 This chapter introduces the basic concepts of dynamical systems theory, and several basic mathematical methods for controlling chaos. The main goal of this chapter is to provide an introduction to and a summary to the theory of dynamical systems with particular emphasis on fractal theory, chaos theory, and chaos control.
Oscar Castillo, Patricia Melin
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Dynamical systems theory for music dynamics
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1995 We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of temporal dynamics in music. (i) Phase space portraits are constructed from the time series wherefrom the dimensionality is evaluated as a measure of the global dynamics of each ...
Boon, Jean-Pierre, Decroly, O.
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Learning Theory for Dynamical Systems
SIAM Journal on Applied Dynamical Systems, 2023 The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then explicitly learning the dynamics from this information.
Tyrus Berry, Suddhasattwa Das
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Dynamical systems theory [PDF]
, 2003 Abstract We have seen examples of dynamical systems for iterated maps and continuous flows. Maps are simpler to analyze numerically and have a rich variety of dynamical behaviors, even in one dimension. By contrast, except in the simplest cases, flows require approximate numerical methods, and in one dimension the solutions cannot do ...
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EXTENDED DYNAMICAL SYSTEMS AND STABILITY THEORY [PDF]
Proceedings of the National Academy of Sciences, 1967 Extended dynamical systems in Banach space and use of invariance principle for stability theory of partial differential ...
Hale, J. K., Infante, E. F.
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Dynamical systems theory in physiology [PDF]
Journal of General Physiology, 2011 Readers of the current issue will find something unfamiliar, perhaps tantalizing, perhaps unsettling. I am referring to the articles by Cha et al. (see [“Ionic mechanisms and Ca2+ dynamics…”][1] and [“Time-dependent changes in membrane excitability…”][2]).
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Spectral Theory of Dynamical Systems
, 2020 This is a survey on spectral theory of dynamical systems.
Kanigowski, Adam, Lemańczyk, Mariusz
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Dynamical theory for adaptive systems [PDF]
Journal of Statistical Mechanics: Theory and ExperimentAbstract The study of adaptive dynamics, involving many degrees of freedom on two separated timescales, one for fast changes of state variables and another for the slow adaptation of parameters controlling the former’s dynamics is crucial for understanding feedback mechanisms underlying evolution and learning.
Pham, Tuan Minh, Kaneko, Kunihiko
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Modern Koopman Theory for Dynamical Systems
SIAM Review, 2022 The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches that formulate models in operator theoretic or probabilistic frameworks.
Steven L. Brunton +3 more
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HOPF ALGEBRAS IN DYNAMICAL SYSTEMS THEORY [PDF]
International Journal of Geometric Methods in Modern Physics, 2007 The theory of exact and of approximate solutions for non-autonomous linear differential equations forms a wide field with strong ties to physics and applied problems. This paper is meant as a stepping stone for an exploration of this long-established theme, through the tinted glasses of a (Hopf and Rota–Baxter) algebraic point of view.
Ebrahimi-Fard, K. +3 more
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