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
A scenario for torus T 2 destruction via a global bifurcation
Tiago Pereira,Tiago Pereira,M.S. Baptista,Marcelo Bussotti Reyes,Iberê L. Caldas,José Carlos Sartorelli,Jürgen Kurths +6 more
TL;DR: In this article, a scenario of a two-frequency torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T 2 with saddle points, creating a heteroclinic saddle connection, is presented.
Journal ArticleDOI
Period Three Implications for Expansive Maps in R N
TL;DR: A multidimensional version of the Li-Yorke cycle coexisting theorem was established for certain (e.g. expansive) maps in this paper, and related fixed-and periodic-point theorems were developed in R n.
An Emergence Principle for Complex Systems
TL;DR: The threshold value, expressed in terms of coupling system parameters, is verified to recovers limits found in a broad range of domains in Physics and Mathematics, giving explicit criterion for emergence in complex system.
Proceedings ArticleDOI
Anti-synchronization of Wang-Chen chaotic systems via sliding mode control
TL;DR: Numerical simulations using MATLAB have been presented in detail to validate the sliding controller design for achieving anti-synchronization of identical Wang-Chen chaotic systems via sliding mode control.
Journal ArticleDOI
Replication of period-doubling route to chaos in impulsive systems
Mehmet Onur Fen,Fatma Tokmak Fen +1 more
TL;DR: In this article, the authors investigate the dynamics of impulsive systems driven by a chaotic system and show that the response impulsive system replicates the sensitivity and the period-doubling cascade of the drive.
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.