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Cellular Neural Networks: Dynamics and Modelling

  • Book
  • © 2003

Overview

Authors:
  1. Angela Slavova

    1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

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Part of the book series: Mathematical Modelling: Theory and Applications (MMTA, volume 16)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
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  2. Basic theory about CNNs

    • Angela Slavova
    Pages 1-48

  3. Dynamics of nonlinear and delay CNNs

    • Angela Slavova
    Pages 49-84

  4. Hysteresis and Chaos in CNNs

    • Angela Slavova
    Pages 85-118

  5. CNN modelling in biology, physics and ecology

    • Angela Slavova
    Pages 118-167

  6. Appendix A. Topological degree method

    • Angela Slavova
    Pages 168-174

  7. Appendix B. Hysteresis and its models

    • Angela Slavova
    Pages 175-188

  8. Appendix C. Describing function method and its application for analysis of Cellular Neural Networks

    • Angela Slavova
    Pages 189-202

  9. Back Matter

    Pages 203-220
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Keywords

About this book

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.

Reviews

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)

Authors and Affiliations

  • Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Angela Slavova

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