A Fundamental Study on Dynamics and Control of Complex Systems

复杂系统动力学与控制的基础研究

基本信息

批准号：
10650236
负责人：
YAGASAKI Kazuyuki
金额：
$ 2.24万
依托单位：
Gifu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10650236/
关键词：
Complex System Chaos Coupled Oscillator Bifurcation Chaos Control Dynamical Systems Theory Hawiltonian System 分岐

项目摘要

In this research, as a fundamental study on dynamics and control of complex systems like atmosphere, life and economic systems, analytical techniques for nonlinear behavior and chaos control methods in coupled oscillators were established as follows.1.For general two-degree-of-freedom dissipative systems with periodic forcing, a theoretical technique to analyze homoclinic and heteroclinic behavior for resonant periodic orbits was proposed and a mechanism for chaos was described.2.For multi-degree-of-freedom Hamiltonian systems with saddle-centers, theoretical techniques to analyze homoclinic and heteroclinic behavior for periodic orbits and invariant tori near the saddle-centers were developed. Applying these techniques, we describe complicated behavior in an infinite-degree-of-freedom model for an unforced and undamped, buckled beam.3.A package of the computer algebra system, Mathematica, to implement necessary computations for the higher-order averaging method, and a driver to a computer software called AUTO for numerical analysis of homoclinic and heteroclinic behavior were developed. Their usefulness was demonstrated for several examples.4.Nonlinear behavior in a forced, simple pendulum and coupled pendula was analyzed theoretically, and the theoretical results were demonstrated in numerical simulations and experiments. Moreover, a two-link robot manipulator was theoretically and numerically proven to exhibit complicated behavior5. Applying improved versions of delayed and external feedback, we performed chaos control in a forced, simple pendulum and coupled pendula, and demonstrated their effectiveness under an influence of noise in numerical simulations and experiments.

In this research, as a fundamental study on dynamics and control of complex systems like atmosphere, life and economic systems, analytical techniques for nonlinear behavior and chaos control methods in coupled oscillators were established as follows.1.For general two-degree-of-freedom dissipative systems with periodic forcing, a theoretical technique to analyze homoclinic and heteroclinic behavior for resonant periodic orbits was proposed and a mechanism对混乱进行了描述。2。对于具有鞍中心的多立方学的哈密顿系统，开发了与鞍中心附近的周期性轨道和不变的Tori分析同质斜切行为的理论技术。应用这些技术，我们描述了无限制的自由度模型中的复杂行为，用于一种未经强制和未固定的，屈曲的光束。3。计算机代数系统（Mathematica）包装，以实现高阶平均方法的必要计算，并将其用于称为Auto的计算机软件的驱动程序，用于AUTO，用于用于同类和Heteroclinic和Heteroclinic行为的数字分析。在理论上分析了几个示例的有用性。4。在强制的，简单的摆和耦合的摆中进行杂音行为，并在数值模拟和实验中证明了理论结果。此外，在理论上和数字上证明了两连锁机器人的操纵器表现出复杂的行为5。应用改进的延迟和外部反馈的版本，我们在强制，简单的摆和耦合的钟摆中进行了混乱控制，并在数值模拟和实验中证明了它们在噪声影响下的有效性。