Nonlinear Dynamics-Adaptive, Learning and Neural Systems

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This co-operative research has been done during the period from May, 1990 to March, 1992. The purpose of the research is to do a systematic research on neurodynamics. The followings are main results obtained in this research :(1) Neurocomputing :Neurocomputing is a style of information processing. An excellent and recent review on neurocomputing is surveyed. In this review, the follwing is emphasized : modern technology has been so developed that neurocomputing can be implemented in computer systems and in neurodevices.(2) Neuron Models and Their Dynamics :Periodic response characteristic of a simple nerve membrane model named two-factor two-mode model stimulated periodically is reported. On the other hand, a model of a chaotic neural network is summarized and its associative dynamics is discussed. Furthermore, dynamical universality of neural networks is reviewed.(3) Mathematical Aspects of Neuro-Dynamics for Combinatorial Optimization and Optimization Algorithms :Hopfield's neural ne … More tworks are known to have a potentiality to solve combinatorial optimization problems. It is, however, found that the networks often fail to get the optimum solution. Mathematical aspects of neuro-dynamics for combinatorial optimization is discussed. Furthermore, two optimization algorithms are presented : The former is an efficient algorithm for finding all of the global minimum points of Hopfiefd's type energy functions ; the latter is the one using Logit transformation.(4) Associative Memory in Neural Networks :A synthesis procedure for a discrete asynchronous neural network is presented. Moreover, the number of stable equilibrium points of a class of Hopfield Networks is developed. On the other hand, an analogy between Markov chain and the asynchronous memory recall process of Hebbian-type associative memory is developed.(5) Applications of Neural Networks to Engineering :Image compression and regeneration by nonlinear associative silicon retina is discussed. Moreover, a cloning template for celluar neural network is reported. Furthermore, separating capabilities of three layer neural networks are surveyed.(6) Dynamics in Nonlinear Networks :An extension of the Lienard theorem and its application is developed. Moreover, mode locking and chaos in a forced self-oscillatory systems with spatial degrees of freedom are discussed.Furthermore, synchronization of chaotic states in a chemical oscillator is discussed.(7) Mathematical analysis of Nonlinear systems :Functional Analysis of nonlinear system fluctuation is developed. Moreover, nonlinear functional analysis and self-validating numerics is reviewed.(8) Holding of open Research MeetingsCo-sponsored by the Technical Group on Nonlinear Problem (NLP) of IEICE and the one on Circuits and Systems (CAS), an open research meeting was held on July 15-17, 1991 at Shikano-shima in Fukuoka. Also on January 31, 1992, second open research meeting was held at Waseda University co-sponsored by NLP and CAS.The special issue of the transactions of IEICE on Nonlinear Theory and Its Applications was published on June, 1991. Also the one on Nonlinear Dynamics-Adaptive, Learning, and Neural Systems will be published on May, 1992. Both of these issues where a main part of the fruits of the research is published are edited by the members of the research. Less