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Replication of Chaos in Neural Networks, Economics and Physics

Marat Akhmet, Mehmet Onur Fen (Autoren)

Buch | Hardcover

XV, 457 Seiten

2015 | 1st ed. 2015
Springer Berlin (Verlag)
978-3-662-47499-0 (ISBN)

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This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.

Prof. Dr. Marat Akhmet is a professor at the Department of Mathematics, Middle East Technical University, Ankara, Turkey. He is a specialist in dynamical models, chaos theory and differential equations. In the last several years, he has been investigating dynamics of neural networks, economic models and mechanical systems. Dr. Mehmet Onur Fen is a postdoctoral researcher at the Department of Mathematics, Middle East Technical University, Ankara, Turkey. His research interests are differential equations, chaos theory and applications to neural networks, economics and mechanical systems.

Introduction.- Replication of Continuous Chaos about Equilibria.- Chaos Extension in Hyperbolic Systems.- Entrainment by Chaos.- Chaotification of Impulsive Systems by Perturbations.- Chaos Generation in Continuous/Discrete-Time Models.- Economic Models with Deterministic Chaos as Generated by Exogenous Continuous/Discrete Shocks.- Replication of Chaos by Neural Networks.- ntrainment by Spatiotemporal Chaos in Glow Discharge-Semiconductor Systems.

"The book presents a systematized and organized exposition of this material, its contextualization within mathematics, science and technology, and a discussion of perspectives for future development. In summary, this monograph provides an overview of results on an aspect of the dynamics of chaotically driven differential equations, such as replication of chaos, which is an interesting issue that goes beyond the research on synchronization and control of chaos that has received so much attention in the last twenty five years." (Jesús M. González-Miranda, Mathematical Reviews, May, 2016)

Erscheint lt. Verlag	21.8.2015
Reihe/Serie	Nonlinear Physical Science
Zusatzinfo	XV, 457 p. 141 illus., 133 illus. in color.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Optik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Deterministic Chaos-Entrainment by Chaos- • Equation-Non-Linear Dynamics-Mechanical • Models-Economic Models • Neural Network-Chaos Control-Chaos • Replication-Differential Equation-Hybrid
ISBN-10	3-662-47499-9 / 3662474999
ISBN-13	978-3-662-47499-0 / 9783662474990
Zustand	Neuware