Replication of Chaos in Neural Networks, Economics and Physics

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Springer, Aug 13, 2015 - Science - 457 pages

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.

 

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Contents

1 Introduction
1
2 Replication of Continuous Chaos About Equilibria
33
3 Chaos Extension in Hyperbolic Systems
101
4 Entrainment by Chaos
126
5 Chaotification of Impulsive Systems
157
6 Chaos Generation in ContinuousDiscreteTime Models
183
7 Economic Models with Exogenous ContinuousDiscrete Shocks
265
8 Chaos by Neural Networks
311
9 The Prevalence of Weather Unpredictability
406
10 Spatiotemporal Chaos in Glow DischargeSemiconductor Systems
441
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About the author (2015)

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.