复杂系统中的自适应性  

Self-adaptability in complex systems

作　　者：李挺[1] 刘曾荣[2] 

机构地区：[1]苏州大学数学科学学院,江苏苏州215006 [2]上海大学非线性科学研究中心,上海200436

出　　处：《浙江师范大学学报（自然科学版）》2006年第4期410-413,共4页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(1037205410171061)

摘　　要：复杂系统的自适应性表现为对应于系统环境的变化,通过调节自身结构或参数作出自适应反应,使得系统对外部环境作出正确、合理的响应.以Lorenz系统为例阐述了这种自适应现象.对于Lorenz系统,通过增加控制器及调整参数,与原来系统相比,得到一个误差系统.当控制器及参数满足一定的条件时,通过构造误差系统的Lyapunov函数,得到误差系统的零解的全局渐进稳定性,从而使调控后的系统与原来系统的解达到同步.Self-adaptability of complex systems was studied. Self-adaptability means that the systems can change its characteristics automatically so that it adapts to the change of environment. Biological system has this kind of properties very obviously. All complex systems have some uncertainness in varying degrees. These uncertainness comes from the external environment, the structure and parameters of systems. Self-adaptability of complex systems shows that when the environment of system was changed, system would make self-adaptability reaction through adjusting its structure and parameters in order that the system could makes correct and reasonable response to the external environment. Taking Lorenz system as an example to explain this kind of self-adaptability. For Lorenz system, through adding controllers and adjusting the parameters, and then comparing with the original ones, an error system can be obtained. When the controllers and parameters satisfy some conditions, Lyapunov function of error system can be constructed. Therefore it was showed that zero solu- tion of error system was global asymptotic stable. Hence synchronization can be achieved for the adjusted system and original system.

关 键 词：复杂系统 LORENZ系统 自适应性 同步 

分 类 号：O175.14[理学—数学]