Replication of Chaos in Neural Networks, Economics and Physics

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.

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

Autorentext

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.

Inhalt
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.