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
Synchronization of switch dynamical systems
TL;DR: The well known synchronization method of Fujisaka and Yamada is adapted to a particular class of piecewise continuous dynamical systems, using the Filippov regularization, and a generalized derivative for the considered class of functions is introduced.
Book ChapterDOI
What Makes a System Complex? - An Approach to Self Organization and Emergence
TL;DR: It is observed that entering complexity state opens the possibility for the function to feedback onto the structure, ie to mimic at technical level the invention of Nature over Her very long history.
Journal ArticleDOI
Simultaneous nonlinear encryption of grayscale and color images based on phase-truncated fractional Fourier transform and optical superposition principle
Xiaogang Wang,Daomu Zhao +1 more
TL;DR: The encryption level of a double random phase encryption based on phase-truncated Fourier transform is enhanced by extending it into fractional Fourier domain and the load of the keys management and transmission is lightened by using CRPMs.
Journal ArticleDOI
Dynamics of coding in communicating with chaos
Erik M. Bollt,Ying-Cheng Lai +1 more
TL;DR: In this article, it was shown that the topological entropy of a chaotic saddle is often less than that of the chaotic attractor and that the chaotic saddle can be robust against noise when the saddle has large noise-resisting gaps covering the phase-space partition.
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.