外激励下两个单向耦合的Lorenz系统的广义同步的复杂性  

Complexity of Generalized Synchronization of Two Unidirectional Coupled Lorenz Systems Under External Excitation

作　　者：陈娟[1] 张荣[1] 徐振源[1] 过榴晓[1] 

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《江南大学学报（自然科学版）》2011年第2期221-231,共11页Joural of Jiangnan University (Natural Science Edition)　

基　　金：国家自然科学基金项目(60875036);国家自然科学青年基金项目(11002061);江南大学创新团队发展计划项目

摘　　要：研究了响应系统在外界周期扰动(外激励)情况下两个单向耦合的Lorenz系统的广义同步问题。利用辅助系统方法,基于稳定性理论得到了两个Lorenz系统达到混沌轨道附近的广义同步时的充分条件以及达到各种复杂周期轨道附近的广义同步时的充分条件。利用广义Hamilton函数理论和Melnikov方法,得到了修正系统进入混沌轨道和各种周期轨道的充分条件,说明广义同步比完全同步更为复杂。数值仿真证实了该方法的可行性及有效性。The generalized synchronization（GS） of two unidirectional coupled Lorenz systems is studied when the response system collapses to external periodic perturbation（external excitation）.Based on the theories of stability,by using method of auxiliary-system,a sufficient criterion is rigorously proven when two Lorenz systems come to generalized synchronization which is near to chaotic orbits and kinds of complicated periodic orbits.Using the Hamilton theorem and Melnikov approach to analyze the modified system,the proofs are proposed when the modified system collapses to chaotic orbits and asymptotically stable limit cycles of different periodic orbits.All of these have shown that generalized synchronization is more complex than complete synchronization.The numerical simulations indicate the effectiveness of the method.

关 键 词：LORENZ系统 辅助系统 单向耦合 广义同步 外激励 

分 类 号：O193[理学—数学]