Overview
- Provides precise definitions of continuous chaos with subsequent theorems on replication of deterministic chaos
- Explains how chaos can be extended through connections in collectives of differential and hybrid equations by the input-output mechanism of chaos
- Opens new perspectives for irregular dynamics of complex systems that are relevant not only in neural networks, economics and mechanics, but also in many other disciplines
- Includes supplementary material: sn.pub/extras
Part of the book series: Nonlinear Physical Science (NPS)
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Table of contents (10 chapters)
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Front Matter
Keywords
About this book
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.
Reviews
“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)
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Replication of Chaos in Neural Networks, Economics and Physics
Authors: Marat Akhmet, Mehmet Onur Fen
Series Title: Nonlinear Physical Science
DOI: https://doi.org/10.1007/978-3-662-47500-3
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2016
Hardcover ISBN: 978-3-662-47499-0Published: 21 August 2015
Softcover ISBN: 978-3-662-51710-9Published: 25 October 2016
eBook ISBN: 978-3-662-47500-3Published: 13 August 2015
Series ISSN: 1867-8440
Series E-ISSN: 1867-8459
Edition Number: 1
Number of Pages: XV, 457
Number of Illustrations: 8 b/w illustrations, 133 illustrations in colour
Additional Information: jointly published with Higher Education Press, Beijing, China
Topics: Applications of Nonlinear Dynamics and Chaos Theory, Difference and Functional Equations, Theoretical and Applied Mechanics, Economic Theory/Quantitative Economics/Mathematical Methods, Mathematical and Computational Biology