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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As perceived, not as known: digital enquiry and the art of intelligence
TL;DR: For example, Heraclitus as mentioned in this paper states that "If you do not expect the unexpected, you will not find it; for it is hard to be sought out and difficult".
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Increasing student interest and comprehension in power engineering at the graduate and undergraduate levels
George G. Karady,G.T. Heydt +1 more
TL;DR: In this article, the authors report on new efforts in the modernization of the basic undergraduate courses and a graduate curriculum in electric power engineering and the main focus of the paper is the modernization in the way power engineering is portrayed to students, and the implementations of changes as those reported here were made at several universities including Arizona State University.
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Multiobjective Optimization of Transformer Design Using a Chaotic Evolutionary Approach
Leandro dos Santos Coelho,Viviana Cocco Mariani,Fabio A. Guerra,Mauricio Valencia Ferreira da Luz,Jean Vianei Leite +4 more
TL;DR: Numerical results of transformer design optimization demonstrate the effectiveness of the proposed CMOA when compared with the UPS-EMOA approach to preserve the diversity of the solutions and find nondominated solutions.
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Complex Intermittency in Switching Converters
TL;DR: The mechanism and conditions for the emergence of intermittency in a common voltage-mode controlled buck converter are explored and it is found that interference at frequencies near the switching frequency or its rational multiples will induce intermittent operation.
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Dynamics of piecewise linear discontinuous maps
TL;DR: The dynamics of maps representing classes of controlled sampled systems with backlash are examined, and it is shown that, depending on the value of the control parameter, all orbits originating in an attractive set are either periodic or dense on the attractor.
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.