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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Book ChapterDOI
Chaos-Based Video Encryption Algorithms
TL;DR: Traditional ciphers like DES, IDEA, RSA, RSA and AES are often used for text or binary data, while not suitable for direct video encryption because of the following reasons.
Journal ArticleDOI
Bifurcations and chaos in convection taking non-Fourier heat-flux
G. C. Layek,N. C. Pati +1 more
TL;DR: In this article, the influence of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation is reported.
Journal ArticleDOI
Adaptive control and synchronization of liu 's four -wing chaotic system with cubic nonlinearity
TL;DR: Wang et al. as discussed by the authors investigated the adaptive chaos control and synchronization of Liu's four-wing chaotic system with cubic nonlinearity and unknown parameters and derived adaptive control laws to achieve global chaos synchronization.
Journal ArticleDOI
Hénon-like attractor in air bubble formation
TL;DR: In this article, the formation of air bubbles in a submerged nozzle in a water/glycerol solution inside a cylindrical tube, submitted to a sound wave perturbation, was observed.
Journal ArticleDOI
Example of robust chaos in a smooth map
M. Andrecut,M. K. Ali +1 more
TL;DR: In this article, a one-dimensional smooth map xt + 1 = f(xt,α) that generates robust chaos in a large domain of the parameter space (α) is presented.
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.