Willamowski-R?9ssler系统混沌行为的数值仿真及控制与同步研究  

NUMERICAL SIMULATION,CONTROL,AND SYNCHRONIZATION RESEARCH ON CHAOTIC BEHAVIOR OF WILLAMOWSKI-R?SSLER SYSTEM

作　　者：孙伟鹏 王贺元[1] 阚猛 

机构地区：[1]辽宁工业大学理学院,锦州121001

出　　处：《动力学与控制学报》2018年第1期35-40,共6页Journal of Dynamics and Control

基　　金：国家自然科学基金(11572146,11526105);辽宁省教育厅科研基金(L2013248);锦州市科技专项基金(13A1D32)资助~~

摘　　要：模拟了Willamowski-R9ssler化学系统经倍周期分岔进入混沌,以及由混沌退化到周期态的全过程.给出了分岔图与最大Lyapunov指数谱和庞加莱截面及功率谱和返回映射图,仿真结果揭示了该系统混沌行为的普适特征.设计了自适应控制器和非线性控制器,通过理论分析及数值仿真实现了对其无量纲化系统的控制.采用驱动-响应的同步方法实现该系统的全局指数同步,数值仿真结果表明该方法是有效的.The whole process of the change of Willamowski-RiSssler chemistry system from period motions to cha- otic motions through double-period bifurcation, as well as the change from chaotic motions to period motions. We present bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system, and the chaotic behavior of the model is also revealed. The adaptive and nonlinear controllers are de- signed, and the theoretical analysis and numerical simulation show that the chaos of the non-dimensional form of Willamowski-R^ssler system can be controlled effectively. Drive-Response method is used to realize the global ex- ponential synchronization. The simulation results show that the Drive-Response method is effective.

关 键 词：化学系统 数值仿真 倍周期分岔 混沌 混沌控制 同步 

分 类 号：O415.5[理学—理论物理]