有关混沌及其控制与同步的一些理解

Understanding of chaos together with its control and synchronization

从实例出发,对非线性耗散系统中的混沌及其控制与同步研究中遇到的有关基本概念和问题作一些哲理性解释。内容涉及混沌的基本假设及其标志性特征、通向混沌的道路、混沌系统的相空间基本格局、混沌控制的基本策略、所谓‘混沌同步’以及‘噪声诱导同步’的实质含意、随机混沌的约定性定义、以及数值仿真在混沌研究中的作用等。对混沌及其控制与同步、以及随机混沌提出了一些独特的新见解。

In this paper philosophical understanding of chaos in nonlinear dissipative systems together with its control and syn- chronization was presented. Included are topics on fundamental underlying assumptions and main characteristics of chaos, the route to chaos, the fundamental pattern of nonlinear chaotic systems in phase space, the fundamental strategy of chaos con- trol, the substance of the so-called ＇chaos synchronization＇ and ＇noise induced synchronization＇, the restricted definition of stochastic chaos, and the function of numerical simulations in studying chaos. Some new unique ideas on chaos, together with its control and synchronization, and stochastic chaos are put forward.