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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The existence and measure of ergodic foliations in Novikov's problem of the semiclassical motion of an electron
TL;DR: In this article, the authors present a selection of the strongest assertions to date concerning the measure and properties of the above zones, which are based on a technique developed by Dynnikov, and have not been stated in earlier publications.
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Dynamical Behavior of q-DEFORMED Henon Map
TL;DR: This paper attempts to numerically analyze the behavior of q-deformed version of Henon map, which is one of the prototypical models exhibiting strange chaotic attractor, and characterize the complete deformation parameter space into different regions corresponding to the periodic and strange chaotic motions.
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Birth of oscillation in coupled non-oscillatory Rayleigh–Duffing oscillators
TL;DR: Hardware experiment is performed on analog circuits simulating RDO model and obtained results confirm the predictions regarding birth of periodic oscillation and other features of system dynamics.
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Integrability analysis of chaotic and hyperchaotic finance systems
TL;DR: In this article, the authors consider two chaotic finance models, namely, the Huang-Li model and the hyper-chaotic model, and show that the former is not integrable in a class of functions meromorphic in variables (x, y, ǫ) for all real values of parameters (a, b, c, d, k).
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Entropy in self-similar shock profiles
TL;DR: In this article, the authors employ the Navier-Stokes equations to construct a self-similar version of Becker's solution for a gaseous shock assuming a particular (physically plausible) Prandtl number; and that solution reproduces the well-known result of Morduchow & Libby that features a maximum of the equilibrium entropy inside the shock profile.
References
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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.