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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Personalized information encryption using ECG signals with chaotic functions
TL;DR: An individual feature of ECG with chaotic Henon and logistic maps for personalized cryptography and an encryption algorithm based on the chaos theory to generate initial keys for chaotic logistic and Henon maps are introduced.
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Controlling chaos and the inverse frobenius–perron problem: global stabilization of arbitrary invariant measures
TL;DR: This work presents a generalization of Baker maps with an arbitrary grammar and whose FP operator is the required stochastic matrix, and reduces the question of stabilizing an arbitrary invariant measure, to the issue of a hyperplane intersecting a unit hyperbox.
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Modeling and nonlinear parameter estimation with Kronecker product representation for coupled oscillators and spatiotemporal systems
Chen Yao,Erik M. Bollt +1 more
TL;DR: In this paper, the authors focus on the question of global modeling, that is, building an ordinary differential equation (ODE) of minimal dimensions which models a given multivariate time dependent data-set.
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A modified adaptive control method for synchronization of some fractional chaotic systems with unknown parameters
S. K. Agrawal,Subir Das +1 more
TL;DR: In this article, a modified adaptive control method is developed and the parameters identification method is then applied in fractional order systems with unknown parameters, and the new modified control method based on Lyapunov stability theory is successfully applied to investigate the synchronization of pair of fractional-order systems amongst Genesio-Tesi, Qi and Chen systems.
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Analogue Electrical Circuit for Simulation of the Duffing-Holmes Equation
TL;DR: In this article, an extremely simple second order analogue electrical circuit for simulating the two-well Duffing-Holmes mathematical oscillator is described, illustrated with the s napshots of chaotic waveforms, with the phase portraits and with the stroboscopic maps.
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.