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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Visualization of Four-Dimensional Spacetimes
TL;DR: In this article, a unified physical basis for special relativistic visualization is established and new and improved methods for the visualization of four-dimensional spacetimes are presented, including texture-based and image-based rendering methods.
Journal ArticleDOI
Bifurcations and chaos in a two-dimensional discrete Hindmarsh–Rose model
TL;DR: In this article, the dynamics of a two-dimensional discrete Hindmarsh-Rose model is discussed, and it is shown that the system undergoes flip bifurcation, Neimark-Sacker bifurbcation, and 1:1 resonance by using a center manifold theorem and bifurlcation theory.
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Fast communication: Spectral properties of chaotic signals generated by the skew tent map
TL;DR: Analytical expressions for the autocorrelation sequence, power spectral density and essential bandwidth of chaotic signals generated by the skew tent map are derived and suggested applications in communication systems are suggested.
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Applications of tripled chaotic maps in cryptography
TL;DR: A new kind of symmetric key block cipher algorithm that is based on tripled chaotic maps is introduced that has many capabilities such as acceptable speed and complexity in the algorithm due to the existence of two coupling parameters and high security.
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Limited Imitation Contagion on Random Networks: Chaos, Universality, and Unpredictability
TL;DR: In this article, the authors study a family of binary state, socially inspired contagion models which incorporate imitation limited by an aversion to complete conformity, and uncover rich behavior in their models whether operating with either probabilistic or deterministic individual response functions on both dynamic and fixed random networks.
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.
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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.