Studies on Analysis of Generation Process of Chaos in Nonlinear Circuits and on Systematic Construction of Chaos Generation Circuits

本合作研究于1988年5月至1990年3月完成。本研究的目的是对工程科学中的混沌现象进行系统的研究。主要研究结果如下：1.非线性电路的性质非线性电阻性电路的解的个数已经阐明了一些重要的性质。一个全局收敛的方法被发现的数值识别分歧的解决方案。此外，还建立了一个检验扩展Libilard系统是否存在混沌的重要判据。2.非线性电路奇异吸引子的结构阐明了锁相环电路、扩展Li6nard电路、某些简单分段线性电路、神经振荡器电路等具有混沌特性的非线性电路。此外，还发展了一些分析非线性电路中奇异吸引子的普适性质的分析方法：余维2分岔理论、同宿连杆理论、Duffing电路的全局分岔结构理论等。3.混沌产生电路的构造阐明了离散动力系统中混沌的详细性质。在此基础上，提出了一种系统地构造嵌入混沌动力系统的混沌发生电路的方法。4. 1989年1月24日至25日，在京都大学举行了由IEICE的非线性问题技术组（NLP）共同主办的公开研究会议。1989年11月20日和21日，在琦玉大学举行了由NLP和CAS共同主办的第二次公开研究会议。5.研究成果的分发IEICE工程混乱交易特刊将于1990年6月出版，由研究人员编辑。在这个问题上，一个主要部分的研究成果将被公布。

This co-operative research has been done during the period from May, 1988 to March, 1990. The purpose of the research is to do a systematic research on chaos in engineering science. The followings are main results obtained by the research: 1. Properties of Nonlinear Circuits A number of important properties have been clarified on the numbers of solutions for nonlinear resistive circuits. A globally convergent method is found for numerically identifying bifurcating solutions. Moreover, an important criterion is established for testing the existence of chaos in an extended Libilard system. 2. Structures of Strange Attractors of Nonlinear Circuits It is clarified that the following nonlinear circuits exhibiting chaos: Phase Locked Loop Circuits, an extended Li6nard circuits, a certain simple piecewise linear circuits, a neural-type oscillator, circuit, etc.. Moreover, a number of analytical methods are developed for analyzing universal properties of strange attractors appearing in nonlinear circuits: a codimension two bifurcation theory, theory of homoclinic linkage, global bifurcation structure theory for the Duffing circuits, etc.. 3. Construction of Chaos Generation Circuits Detailed properties are clarified for chaos in discrete dynamical systems. Based on this result, systematic methods of constructing chaos generation circuits are proposed in which chaotic dynamical systems are imbedded. 4. Holding of Open Research Meetings Cosponsored by the Technical Group on Nonlinear Problems (NLP) of IEICE, an open research meeting was held on January 24 and 25, 1989 at Kyoto University. Also on November 20 and 21, 1989 second open research meeting was held at Saitama University cosponsored by NLP and CAS. 5. Distribution of Fruits of the Research The special issue of the transactions of IEICE on Engineering Chaos will be published on June, 1990, which is edited by the members of the research. In this issue, a main part of the fruits of the research is to be published.