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Study on Methods of Analysis of Nonlinear Circuits with Symmetrical Structure

对称结构非线性电路分析方法研究

基本信息

批准号：
08650431
负责人：
KAWAKAMI Hiroshi
金额：
$ 0.83万
依托单位：
The University of Tokushima
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1997
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08650431/
关键词：
Coupled Oscillators Synchronization Bifurcation Phenomena Symmetry of Circuit Representation of Group In Phase Oscillations Synchronization to Chaos Asynchronous Quasi-periodic Oscillations 多相振動

项目摘要

State of nonlinear circuits with symmetrical structure has two orbits : one is determined by its dynamical system and the other by the group action correlated with symmetry. In this research we tried to develop numerical methods of analysis for such systems with symmetry. By using these methods we analyzed the global bifurcation of limit cycles in coupled oscillators with a ring, symmetry breaking bifurcations of coupled oscillators with a prescribed group connection, etc.1. Analysis of a unidirectional and/or bidirectional coupled oscillators. We found that the different couplings cause different types of multi-phase oscillations, such as in-phase, anti-phase, or tri-phase oscillations. The Hopf bifurcation of equilibrium points and the Neimark-Sacker bifurcation of limit cycles are studied and chaotic states are obtained by symmetry breaking.2. Codimension two or three bifurcations correlated with symmetry are studied and some methods of numerical analysis for finding these degenerate bifurcation points are developed.3. Oscillations of neural networks coupled as linear and ring connections are investigated. Some chaotic itinerary are analyzed as a global bifurcation of invariant manifolds.4. Forced synchronization of coupled oscillators are studied. By injecting sinusoidal input we found the bifurcational properties of synchronized states with in phase and/or anti-phase.5. Some interrupted nonlinear circuits are analyzed by using the same method of numerical analysis. We found simple three dimensional systems with chaotic states interrupted by periodic switching action.6. The booklet is published in which main results are collected together.

具有对称结构的非线性电路的状态有两个轨道：一个轨道由其动力学系统决定，另一个轨道由与对称性相关的群作用决定。在这项研究中，我们试图发展这种系统的对称性分析的数值方法。利用这些方法，我们分析了带环耦合振子极限环的全局分支、带给定群联络耦合振子的对称破缺分支等。单向和/或双向耦合振荡器的分析。我们发现，不同的耦合导致不同类型的多相振荡，如同相，反相，或三相振荡。研究了系统平衡点的Hopf分支和极限环的Neimark-Sacker分支，并通过对称破缺得到了系统的混沌态.研究了与对称性相关的余维二分叉和余维三分叉，并给出了寻找这些退化分叉点的数值分析方法.研究了线性和环形耦合神经网络的振荡问题。将某些混沌轨迹分析为不变流形的全局分支.研究了耦合振子的强迫同步问题。通过注入正弦输入，我们发现了同步态的同相和/或反相分岔特性。用同样的数值分析方法分析了一些非线性间断电路。我们发现简单的三维系统的混沌状态中断周期性开关动作。出版了一本小册子，其中收集了主要结果。