Control of Codimension-2 Bautin Bifurcation in Chaotic Lü System  

作　　者：LU Zhuo-Sheng DUAN Li-Xia 

机构地区：[1]School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China [2]School of Science, North China University of Technology, Beijing 100041, China

出　　处：《Communications in Theoretical Physics》2009年第10期631-636,共6页理论物理通讯（英文版）

基　　金：Supported by the National Nature Science Foundation of China (NSFC) under Grant No.60772023;Li-Xia Duan wishes to acknowledge the support from NSFC under Grant No.10872014

摘　　要：In this paper, we design a feedback controller, and analytically determine a control criterion so as to control the codimension-2 Bautin bifurcation in the chaotic Lfi system. According to the control criterion, we determine a potential Bautin bifurcation region （denoted by P） of the controlled system. This region contains the Bautin bifurcation region （denoted by Q） of the uncontrolled system as its proper subregion. The controlled system can exhibit Bautin bifurcation in P or its proper subregion provided the control gains are properly chosen. Particularly, we can control the appearance of Bautin bifurcation at any appointed point in the region P. Due to the relationship between Bantin bifurcation and Hopf bifurcation, the control scheme thereby is also viable for controlling the creation and stability of the Hopf bifurcation. In the controller, there are two terms： a linear term and a nonlinear cubic term. We show that the former determines the location of the Hopf bifurcation while the latter regulates its criticality. We also carry out numerical studies, and the simulation results confirm our analyticai predictions.

关 键 词：LU system bifurcation control Bautin bifurcation Hopf bifurcation 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置] O322[自动化与计算机技术—控制科学与工程]