受控Lorenz系统的一些结果及其应用  

Some results of controlled Lorenz system and their application

作　　者：张树来[1] 田立新[1] 杨广娟[1] 

机构地区：[1]江苏大学非线性科学研究中心,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2006年第5期458-462,共5页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(100710331);江苏省自然科学基金资助项目(BK2002003)

摘　　要：首先考虑受控的Lorenz系统,利用Jacobin矩阵和平衡点的定义,给出了系统的控制项;再利用广义Lyapunov函数簇,给出了此系统的全局吸引集和正向不变集估计的方法和结果,并分析了此系统的稳定性;利用此系统简化椭球公式的证明,从而证明了Leonov公式,将估计式统一在一个公式之中,新公式还可以派生出一系列其他的估计式;然后,利用几何学的交集的思想,获得全局吸引集和正向不变集的更佳结果;最后,采用线性反馈的方法构造了一个同步系统,在Matlab上进行了数值仿真,给出了系统的同步误差图,结果表明此方法是可行有效的.The controlled Lorenz system is considered firstly, and the control term of the system is given with the sense of the Jacobin matrix and the definition of the balanced point. Then, these methods and results of the global attractive set and positive invariant set irt the system are delivered with the generalized Lyapunov function family. The stability of the system is discussed. Leonov formula is proved by predigesting the proof of the ellipsoid formulas. Some estimable formulas are put in one formula, The new formula will derive a group of other estimable formulas. Then, these better results of the global attractive set and positive invariant set are obtained with the thought of intersection in geometry theory. Finally, a linear feedback synchronization approach for the chaotic system is presented, and a simulation is conducted with Matlab to prove synchronous validity and these figures of synchronous errors are given. The simulation results indicate that the method is feasible and effective.

关 键 词：LORENZ混沌系统 全局吸引集 正向不变集 全局指数同步 LYAPUNOV函数 

分 类 号：TP271[自动化与计算机技术—检测技术与自动化装置]