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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Bifurcation behaviour in parallel‐connected boost converters
TL;DR: It is found that variation of some parameters leads to Neimark–Sacker bifurcation in a system of parallel-connected d.c./d.c. boost converters.
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Immunization strategy for epidemic spreading on multilayer networks
TL;DR: A targeted immunization strategy for epidemic spreading over a multilayer network is studied and it is found that the targeted strategy is not as efficient as in isolated networks, due to the fact that in order to stop the spreading of the disease it is necessary to immunize more than the 80 % of the individuals.
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Analysis of chaotic saddles in high-dimensional dynamical systems: the Kuramoto-Sivashinsky equation.
TL;DR: A novel technique is described that uses the stable manifold of a chaotic saddle to characterize the homoclinic tangency responsible for an interior crisis, a chaotic transition that results in the enlargement of a Chaos attractor.
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A chaotic attractor in ecology: theory and experimental data
Jim M. Cushing,Shandelle M. Henson,Robert A. Desharnais,Brian Dennis,R. F. Costantino,Aaron A. King +5 more
TL;DR: In this article, a deterministic LPA model was used to predict the behavior of a population of flour beetles (Tribolium castaneum) in controlled laboratory experiments, including a specific route to chaos.
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Stability Analysis of Distributed Order Fractional Chen System
TL;DR: Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractions of Chen system is discussed and chaos exists in the double fractional order Chen system.
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.