Nonlinear Dynamics-Adaptive, Learning and Neural Systems

这项合作研究是在1990年5月至1992年3月期间进行的。本研究的目的是对神经动力学进行系统的研究。(1)神经计算：神经计算是一种信息处理方式。对神经计算的一篇优秀的最新评论进行了综述。本文着重介绍了现代技术的发展，使得神经计算可以在计算机系统和神经设备中实现。(2)神经元模型及其动力学：周期性刺激的简单神经膜模型的周期反应特性--双因素双模模型。另一方面，总结了一种混沌神经网络模型，并讨论了其联想动力学。(3)组合优化神经动力学的数学问题和优化算法：Hopfield的Ne-…神经网络更多的网络被认为具有解决组合优化问题的潜力。然而，人们发现网络往往得不到最优解。讨论了用于组合优化的神经动力学的数学方面。提出了两种优化算法：前者是寻找Hopfiefd型能量函数全局极小点的有效算法，后者是基于Logit变换的优化算法。(4)神经网络中的联想记忆：给出了离散异步神经网络的一种综合方法。此外，还给出了一类Hopfield网络的稳定平衡点个数。另一方面，将马尔可夫链与Hebbian型联想记忆的异步记忆回忆过程进行了类比。(5)探讨了神经网络在工程中的应用：非线性联想硅视网膜的图像压缩与再生。此外，还报道了一种用于细胞神经网络的克隆模板。此外，还考察了三层神经网络的分离能力。(6)非线性网络中的动力学：推广了Lienard定理及其应用。此外，还讨论了空间自由度强迫自振荡系统中的锁模和混沌问题，并讨论了化学振子中混沌态的同步问题。(7)非线性系统的数学分析：发展了非线性系统涨落的泛函分析。此外，还对非线性泛函分析和自验证数值计算进行了评述。(8)由IEICE非线性问题技术小组(NLP)和电路与系统技术小组(CAS)共同主办的公开研究会议于1991年7月15-17日在福冈柴野岛举行。1992年1月31日，由NLP和CAS共同主办的第二次公开研究会议在早稻田大学举行。1991年6月，IEICE非线性理论及其应用汇刊特刊出版。还有一本关于非线性动力学--自适应、学习和神经系统的书将于1992年5月出版。这两期杂志发表了研究成果的主要部分，由研究成员编辑。较少

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