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
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Toward a Theory of Chaos
TL;DR: In this paper, a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of functions in an extended multifunction space, and the topological theory of convergence is proposed.
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The analysis of chaotic time-series data
TL;DR: A brief survey of time-series analysis methods that are applicable to processes whose behavior can be described as low-dimensional chaos can be found in this article, where the goal is to allow experimentalists to obtain local estimates of the dynamics directly from a set of data.
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The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation.By Gary William Flake
TL;DR: In the early 1970s, it was not a profound discovery of a secret hidden from the uninitiated, a rite of passage through which every young mathematician must go.
The glue of (ab)normal mental life: Networks of interacting thoughts, feelings and behaviors
TL;DR: Cramer et al. as discussed by the authors proposed a method to visualize comorbidity networks and, based on an empirical network for major depression and generalized anxiety, they argue that this approach generates realistic hypotheses about pathways to comorrbidity, overlapping symptoms, and diagnostic boundaries, that are not naturally accommodated by latent variable models.
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Adaptive projective synchronization between different chaotic systems with parametric uncertainties and external disturbances
TL;DR: Based on Lyapunov stability theory, the projective synchronization between a pair of different chaotic systems with fully unknown parameters are derived such that the chaotic response system controls the chaotic drive 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.