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
Cryptanalyzing a discrete-time chaos synchronization secure communication system
TL;DR: It is shown that the security is compromised even without precise knowledge of the chaotic system used, and many suggestions to improve its security in future versions are made.
Book ChapterDOI
Hybrid Synchronization of Hyperchaotic Qi and Lü Systems by Nonlinear Control
TL;DR: Nonlinear control is the method used for the Hybrid synchronization of identical hyperbolic Qi systems and hybrid synchronization of hyperchaotic Qi and Lu systems and this method is effective and convenient to achieve hybrid synchronization of the two hyperchaotics.
Journal ArticleDOI
Dynamics of current-based, Poisson driven, integrate-and-fire neuronal networks
Katherine A. Newhall,Gregor Kovačič,Peter Kramer,Douglas Zhou,Aaditya V. Rangan,David Cai,David Cai +6 more
TL;DR: In this article, synchronous total firing events, during which all the neurons fire simultaneously, are observed using numerical simulations and found to be the attracting state of the network for a large range of parameters.
Journal ArticleDOI
Arithmetic coding as a non-linear dynamical system
TL;DR: In this article, a generalization of GLS to piecewise non-linear maps (Skewed-nGLS) has been proposed and used for joint source coding and encryption.
Journal ArticleDOI
Chaos and order in biomedical rhythms
TL;DR: An overview of nonlinear dynamics and chaos concepts useful for the analysis of biomedical system and some characteristics of normal and pathological responses are discussed.
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.