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
Nonlinear instabilities in TCP-RED
TL;DR: This work develops a discrete-time dynamical feedback system model for a simplified TCP network with RED control and provides a nonlinear analysis that can help in understanding observed parametric sensitivities.
Journal ArticleDOI
Global chaos synchronization of hyperchaotic pang and hyperchaotic wang systems via adaptive control
TL;DR: Adaptive control method is deployed in this paper for the general case when the system parameters are unknown and the Lyapunov exponents are not required for these calculations.
Book ChapterDOI
Global Chaos Synchronization of Hyperchaotic Lorenz Systems by Sliding Mode Control
TL;DR: Numerical simulations are shown to illustrate and validate the sliding mode control results derived in this paper for the identical hyperchaotic Lorenz systems.
Journal ArticleDOI
Toward a Theory of Borders in Motion
TL;DR: In this paper, a theory of borders in motion is proposed, and three component realms of a conceptual framework are offered: generation and realization of borders through dichotomization and dialecti...
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.