Chaos in a manifold piecewise linear system
Chaos in a manifold piecewise linear system
复制标题
流形分段线性系统中的混沌
DOI：
10.1002/ecja.4410641003
复制
发表时间：
1981
期刊：
影响因子：
--
通讯作者：
H. Fujita
中科院分区：
文献类型：
--
作者：
Toshimichi Saito;H. Fujita
本文描述了一类微分方程解的不规则性。这种现象被称为混沌，在普通的自微分方程中，当用正型表示时，它发生在三维之外。本文提出了一种新的微分方程，称为流形分段线性方程组来处理这种现象。该方程用线性系统的特殊耦合来描述，并从严格得到的局部解出发，严格计算了一个用于研究解行为的庞加莱映射。因此，用解析的方法来处理目前无法处理的微分方程的混沌成为可能。微分方程的解在某一参数区域内表现为非周期，既不收敛也不发散。这个方程可以用相同形式的不同参数的庞加莱映射作为一个整体来分析。这是敏感性分析所需要的。对于给定的参数和定义区域，用不同的形式表示庞加莱映射，并给出了与前人研究相对应的一个例子。
This paper describes the irregular behavior of solutions to certain differential equations. This phenomenon is called chaos and in ordinary automomous differential equations it occurs beyond three dimensions when represented by normal type. The authors propose here a new differential equation, called the manifold piecewise linear system, in dealing with this phenomenon. The equation is described by special coupling of the linear system and, from the local solution rigorously obtained, a Poincare map for investigation of the solution behaviors is calculated rigorously. Thus, an analytical approach to the chaos of differential equations which cannot be dealt with at the present becomes possible. The differential equation solution is shown in a certain parameter region to become aperiodic and is neither convergent nor divergent. This equation can be analyzed as a whole by the Poincare map in terms of the different parameters with the same form. This is desirable for sensitivity analysis. Also, for a given parameter and region of definition, Poincare maps are expressed in terms of different forms and an example corresponding to previous research is presented.