Cellular Neural Networks: Dynamics and Modelling

ISBN-13: 9789048162543 / Angielski / Miękka / 2010 / 220 str.

A. Slavova

Opis

This book deals with new theoretical results for studying Cellular Neural Networks (CNNs) concerning its dynamical behavior. New aspects of CNNs' applications are developed for modelling of some famous nonlinear partial differential equations arising in biology, genetics, neurophysiology, physics, ecology, etc. The analysis of CNNs' models is based on the harmonic balance method well known in control theory and in the study of electronic oscillators. Such phenomena as hysteresis, bifurcation and chaos are studied for CNNs.

The topics investigated in the book involve several scientific disciplines, such as dynamical systems, applied mathematics, mathematical modelling, information processing, biology and neurophysiology. The reader will find comprehensive discussion on the subject as well as rigorous mathematical analyses of networks of neurons from the view point of dynamical systems. The text is written as a textbook for senior undergraduate and graduate students in applied mathematics. Providing a summary of recent results on dynamics and modelling of CNNs, the book will also be of interest to all researchers in the area.

Recenzje

From the reviews:

"In 1988, Chua and Yang introduced a novel class of information processing systems, termed cellular neural networks (CNNs) ... . The book under review is concerned with mathematical modeling and analysis of this useful class of neural networks ... . the book contains many interesting theoretical results on dynamics of CNNs along with examples illustrating the usefulness of CNNs for mathematical modeling in natural sciences and may be of interest for researchers and graduate students in applied mathematics." (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1049 (24), 2004)

Spis treści

Preface. 1: Basic theory about CNNs. 1.1. Introduction to the CNN paradigm. 1.2. Main types of CNN equations. 1.3. Theorems and results on CNN stability. 1.4. Examples. 2: Dynamics of nonlinear and delay CNNs. 2.1. Nonlinear CNNs. 2.2. CNN with delay. 2.3. Examples. 3: Hysteresis and chaos in CNNs. 3.1. CNNs with hystersis in the feedback system. 3.2. Nonlinear CNNs with hysteresis in the output dynamics. 3.3. Feedback and hysteresis. 3.4. Control of chaotic CNNs. 4: CNN modelling in biology, physics and ecology. 4.1. Modelling PDEs via CNNs. 4.2. CNN model of Sine-Gordon equation. 4.3. CNN model of FitzHugh-Nagumo equation. 4.4. CNN model of Fisher's equation. 4.5. CNN model of Brusselator equation. 4.6. CNN model of Toda Lattice equation. 4.7. Lotka-Volterra equation and its CNN model. 5: Appendix A: Topological degree method. 6: Appendix B: Hysteresis and its models. 7: Appendix C: Describing function method and its application for analysis of Cellular Neural Networks. References. Index.