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
More filters
Journal ArticleDOI
Regulation and controlled synchronization for complex dynamical systems
TL;DR: In this article, the authors investigated the problem of controlled synchronization as a regulator problem and found a (output) feedback controller that achieves matching between the transmitter and the controlled receiver, where the standard solvability assumptions for the regulator problem are not met.
Book ChapterDOI
Multimedia Security: A Survey of Chaos-Based Encryption Technology
TL;DR: In the recent years, with the development of network and multimedia technology, multimedia data, especially image, audio and video data, is used more and more widely in human society and cryptology has been employed in many practical applications.
Journal ArticleDOI
Nonlinear dynamic analysis of an optimal particle damper
TL;DR: In this paper, a single degree of freedom mechanical system with a particle damper was studied and the particle damping was optimized for the primary system operating condition by using an appropriate gap size for a prismatic enclosure.
Journal ArticleDOI
Feature Matching in Time Series Modeling
Yingcun Xia,Howell Tong +1 more
TL;DR: In this paper, the authors argue that the shortcomings need not always be due to the model formulation but the inadequacy of the conventional fitting methods, and they prefer an alternative approach to conventional model fitting that typically involves one-step-ahead prediction errors.
Journal ArticleDOI
Chaos and flights in the atom-photon interaction in cavity QED.
TL;DR: It is demonstrated how the atom-photon dynamics with a given value of alpha depends on the values of delta and initial conditions, which can be used to find new ways to manipulate atoms, to cool and trap them by adjusting the detuning delta.
References
More filters
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.