复杂动力系统初探

探讨传统动力系统与复杂系统之间的关系，并指出某些系统确实具有复杂系统的明显特征，首先研究切换系统，指出这种系统具有1＋1≠2的的特征，并进一步研究这种系统的一些特点，其次，考虑一类动力系统的演化模型，指出这种系统改变着自己的环境和形态，但某些性质不变，将其称为遗传性质，这是我们用严格数学理论与动力系统理论研究复杂系统的尝试。

Exploring Complex Dynamic Systems

This paper reveals some relationship between the traditional dynamic systems and the complex systems, and shows that there are some dynamic systems, which do propose some significant properties of complex systems. First, a kind of switching systems is investigated. It is revealed that such systems do have the property that 1+1≠2. Some further properties of such systems are presented as well. Secondly, an evolution model of dynamic system is considered. We show that such a system is changing its environment and style etc., while some other properties remain unchanged. We call such properties the genetic properties. The research conducted in this paper is the first step of our effort to investigate the complex systems via rigorous mathematical tools and the dynamic system theory.