Cellular Neural Networks: Dynamics and Modelling: 16 (Mathematical Modelling: Theory and Applications, 16) - Hardcover

Slavova, A.

Hardcover

ISBN 10: 140201192X ISBN 13: 9781402011924

Publisher: Springer, 2003

Synopsis

Conventional digital computation methods have run into a se­ rious speed bottleneck due to their serial nature. To overcome this problem, a new computation model, called Neural Networks, has been proposed, which is based on some aspects of neurobiology and adapted to integrated circuits. The increased availability of com­ puting power has not only made many new applications possible but has also created the desire to perform cognitive tasks which are easily carried out by the human brain. It become obvious that new types of algorithms and/or circuits were necessary to cope with such tasks. Inspiration has been sought from the functioning of the hu­ man brain, which led to the artificial neural network approach. One way of looking at neural networks is to consider them to be arrays of nonlinear dynamical systems that interact with each other. This book deals with one class of locally coupled neural net­ works, called Cellular Neural Networks (CNNs). CNNs were intro­ duced in 1988 by L. O. Chua and L. Yang [27,28] as a novel class of information processing systems, which posseses some of the key fea­ tures of neural networks (NNs) and which has important potential applications in such areas as image processing and pattern reco­ gnition. Unfortunately, the highly interdisciplinary nature of the research in CNNs makes it very difficult for a newcomer to enter this important and fasciriating area of modern science.

About this title

Review

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)

Synopsis

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.

Edition details

• Publisher: Springer
• Publication date: 2003
• Language: English
• ISBN 10: 140201192X
• ISBN 13: 9781402011924
• Binding: Hardcover
• Number of pages: 230