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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Using dynamical systems tools to detect concept drift in data streams
TL;DR: A new approach to detect concept drifts on data streams using dynamical systems and chaos theory surpasses traditional ones and the modeling of determinism and stochasticity improves concept drift detection.
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Evolutionary dynamics can be chaotic: A first example
TL;DR: This paper considers a Lotka–Volterra tritrophic food chain composed of a resource, its consumer, and a predator species, each characterized by a single adaptive phenotypic trait, and shows that for suitable modeling and parameter choices the evolutionary trajectories approach a strange attractor in the three-dimensional trait space.
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Toward the Use of Chua's Circuit in Education, Art and Interdisciplinary Research: Some Implementation and Opportunities
TL;DR: This paper considers the merging of Chaos with art, including such forms as digital images, sounds and music, based on dynamic systems derived from Chua's Circuit and using appropriate coding methods, to foster a deeper understanding of the evolution of dynamic systems through computer simulation.
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Real Arnold complexity versus real topological entropy for birational transformations
TL;DR: In this paper, a family of birational transformations of two variables, depending on one parameter, for which simple rational expressions with integer coefficients, for the exact expression of the dynamical zeta function, have been conjectured.
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Can a chaotic solution in the QCD evolution equation restrain high-energy collider physics?
TL;DR: In this article, the random aperiodic oscillation of the gluon distributions in a modified Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation has positive Lyapunov exponents.
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.