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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Dynamical behaviors and chaos control in a discrete functional response model
TL;DR: In this paper, the dynamical behaviors and chaos control in a discrete functional response model are investigated in a chaotic system, where a controller is designed to stabilize the chaotic orbits and enable them to be an ideal target one (i.e., an unstable fixed point of the chaotic system).
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Fractal analysis of the structure and dynamics of a satellite-detected urban heat island
TL;DR: In this article, three fractal models-surface, profile and pixel models-were developed to analyse the structure and dynamics of an urban heat island (UHI), which were tested using data from Shanghai taken in 1990, 1995 and 1998.
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Firing patterns in a conductance-based neuron model: bifurcation, phase diagram, and chaos
TL;DR: Wilson’s conductance-based neocortical neuron model, derived from the Hodgkin–Huxley model, is explored to understand underlying mechanisms of the firing patterns, and phase diagrams describing boundaries between the domains of different firing patterns are obtained.
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Inverse limits, economics, and backward dynamics
Judy Kennedy,Judy Kennedy +1 more
TL;DR: The authors survey recent papers on the problem of backward dynamics in economics, providing along the way a glimpse at the economics perspective, a discussion of the economic models and mathematical tools involved, and a list of applicable literature in both mathematics and economics.
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.