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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Time series prediction using Lyapunov exponents in embedding phase space
TL;DR: A novel method of chaotic time series prediction, which is based on the fundamental characteristic of chaotic behavior that sensitive dependence upon initial conditions (SDUIC), and Lyapunov exponents (LEs) is a measure of the SDUIC in chaotic systems is proposed.
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Pathway selection's utility for control of word recognition.
Patrice Gibbs,Guy C. Van Orden +1 more
TL;DR: In this paper, word regularity effects were tested in three lexical decision experiments using several definitions of word normality, and the observed pattern corroborated a resonance account with parametric control.
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Using artificial neural networks to forecast chaotic time series
TL;DR: From the very good forecasting results it can be concluded that neural networks can be considered to be an important tool for making predictions of the time evolution of nonlinear systems.
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Parallel chaotic hash function based on the shuffle-exchange network
TL;DR: Results show that the proposed design has strong security strength with near-perfect statistical qualities and fast hashing speed that surpasses both chaotic hash functions and the MD5 hash function.
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Spurious structures in chaos indicators maps
TL;DR: In this paper, the influence of the initial variations vector is explained in the context of Lyapunov vectors theory and some selection rules are recommended for spectral and variational methods.
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.
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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.