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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Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps
TL;DR: In this paper, the authors extend these ideas to hyperbolic maps in higher dimensions and apply a new procedure called "unwrapping" to regularised versions of the eigendistributions to reveal the geometric structures associated with almost-invariant dynamics.
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Numerical analysis of the friction-induced oscillator of Duffing's type with modified LuGre friction model
Danylo Pikunov,Andrzej Stefanski +1 more
TL;DR: In this paper, an analysis of a friction-induced mechanical oscillator with cubic nonlinearity and an applied dynamical model of dry friction is presented. And the Lyapunov exponents spectrum of the frictional oscillator is calculated by means of a recently implemented method of their estimation for non-smooth systems.
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Is Prediction Possible? Chaotic Behavior of Multiple Equilibria Regulation Model in Cellular Automata Topology
TL;DR: The theoretical hypothesis that the urge for “prediction” in social sciences should be reconsidered in terms of “predictability horizon” is argued, because the system is not only unpredictable on the long run but, in addition, it will never rest in a final steady state.
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Characterization of the local instability in the Hénon-Heiles Hamiltonian
TL;DR: Several prototypical distributions of finite-time Lyapunov exponents have been computed for the two-dimensional Henon-Heiles Hamiltonian system as discussed by the authors, and different shapes are obtained for each dynamical state.
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A method for estimating stochastic noise in large genetic regulatory networks
TL;DR: This paper presents an algorithm, based on error growth techniques from non-linear dynamics, to rapidly estimate the noise characteristics of genetic networks of arbitrary size.
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.