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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Explicit solutions and stability analysis of the (2 + 1) dimensional KP-BBM equation with dispersion effect
Asish Ganguly,Amiya Das +1 more
TL;DR: It is proved that in the presence of dispersion effect on the equation, yet there exists bounded traveling wave solutions in different classes in terms of solitary waves, periodic and elliptic functions in certain regions.
Journal ArticleDOI
Fully programmable, scalable chaos-based PN sequence generation
TL;DR: An efficient technique for chaos-based pseudonoise sequence generation is presented and the results show that the generated sequences possess statistical characteristics similar to other PN sequences.
Journal ArticleDOI
Localization of periodic orbits of the Rössler system under variation of its parameters
TL;DR: In this article, the localization problem of compact invariant sets of the Rossler system is considered, and the main interest is attracted to a localization of periodic orbits, where the authors establish a number of algebraic conditions imposed on parameters under which the system has no compact invariants contained in half-spaces z > 0; z < 0; and in some others.
Proceedings ArticleDOI
Design of a generalized bidirectional tent map suitable for encryption applications
TL;DR: This paper investigates a set of four generalized tent maps where the conventional map is a special case and the proposed maps have extra degrees of freedom which provide different chaotic characteristics and increase the design flexibility required for many applications.
Journal ArticleDOI
Transitivity implies period six: A simple proof
Chun Hung Hsu,Ming-Chia Li +1 more
TL;DR: An elementary proof of the result that any continuous and transitive interval map must have a period-6 cycle is given and it is shown by example that six is the maximal period (in the Sharkovsky ordering) that transitivity can imply.
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.