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。本研究的主要成果如下：(1)神经计算：神经计算是一种信息处理方式。本文综述了最近关于神经计算的一篇优秀的综述。在这篇综述中，强调了以下几点：现代技术的发展使得神经计算可以在计算机系统和神经装置中实现。(2)神经元模型及其动力学：报道了一种简单的双因子双模周期性刺激神经膜模型的周期响应特性。另一方面，总结了混沌神经网络的模型，并讨论了其关联动力学。此外，还对神经网络的动态通用性进行了评述。(3)组合优化和优化算法的神经动力学的数学方面：Hopfield的神经网络…更多的网络被认为具有解决组合优化问题的潜力。然而，我们发现网络往往不能得到最优解。讨论了组合优化的神经动力学数学问题。进一步给出了两种优化算法：前者是一种求Hopfiefd型能量函数全局所有极小点的高效算法；后者是使用Logit变换的。(4)神经网络中的联想记忆：给出了离散异步神经网络的综合过程。此外，给出了一类Hopfield网络稳定平衡点的个数。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类比。(5)神经网络在工程中的应用：讨论了基于非线性关联硅视网膜的图像压缩与再生。此外，还报道了细胞神经网络的克隆模板。进一步研究了三层神经网络的分离能力。(6)非线性网络动力学：给出了Lienard定理的推广及其应用。此外，还讨论了具有空间自由度的强迫自振荡系统的模态锁定和混沌问题。进一步讨论了化学振荡器中混沌态的同步问题。(7)非线性系统的数学分析：发展了非线性系统波动的泛函分析。此外，还对非线性泛函分析和自验证数值进行了综述。(8)开放研究会议的召开由IEICE非线性问题技术小组（NLP）和电路与系统技术小组（CAS）共同主办的开放研究会议于1991年7月15日至17日在福冈鹿野岛召开。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召开。1991年6月出版了《国际电工工程学会学报：非线性理论及其应用》特刊。另一篇关于非线性动力学——自适应、学习和神经系统的论文将于1992年5月发表。这两个问题都是研究成果的主要部分，由研究人员编辑出版。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