Open AccessBook
Chaos: An Introduction to Dynamical Systems
TLDR
One-dimensional maps, two-dimensional map, fractals, and chaotic attraction attractors have been studied in this article for state reconstruction from data, including the state of Washington.Abstract:
One-Dimensional Maps.- Two-Dimensional Maps.- Chaos.- Fractals.- Chaos in Two-Dimensional Maps.- Chaotic Attractors.- Differential Equations.- Periodic Orbits and Limit Sets.- Chaos in Differential Equations.- Stable Manifolds and Crises.- Bifurcations.- Cascades.- State Reconstruction from Data.read more
Citations
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Journal ArticleDOI
Mean field dynamics of random Boolean networks
TL;DR: In this article, it was shown that the dynamical evolution of random Boolean networks can be described by a family of polynomial maps, and that the dynamics of two stochastic coupled networks can also be represented by two deterministic coupled maps.
Journal ArticleDOI
B-spline neural network design using improved differential evolution for identification of an experimental nonlinear process
TL;DR: The numerical results presented here indicate that chaotic DE was effective for building a good BSNN model for the nonlinear identification of an experimental nonlinear yo-yo motion control system.
Book ChapterDOI
From Deterministic Chaos to Anomalous Diffusion
TL;DR: In this paper, the authors introduce deterministic chaos in one-dimensional maps in form of Ljapunov exponents and dynamical entropies, and show the escape rate formalism for deterministic diffusion, which expresses the diffusion coefficient in terms of the above two chaos quantities.
Proceedings ArticleDOI
A control perspective on communication using chaotic systems
TL;DR: It is shown that a synchronization-based scheme for secure communication described in the literature may in fact be interpreted as an adaptive identification scheme.
Journal ArticleDOI
Using State Space Grids for Modeling Temporal Team Dynamics
TL;DR: The potential of dynamics systems theory for researching team processes is outlined and how state space grids, as a methodological application rooted in the dynamic systems perspective, can help build new knowledge about temporal team dynamics is highlighted.
References
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Journal ArticleDOI
Synchronization in chaotic systems
TL;DR: This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.
Journal ArticleDOI
The Fractal Geometry of Nature
TL;DR: A blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) is presented in this article.
Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.