Replication of Chaos in Neural Networks, Economics and Physics

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)