含分散时滞反馈的Chen系统的分支分析  

Bifurcation Analysis for Chen's System with Distributed Delays Feedback

作　　者：管俊彪[1] 陈芳跃[2] 

机构地区：[1]上海大学数学系,上海200444 [2]浙江师范大学数理学院,金华321004

出　　处：《数学学报（中文版）》2007年第1期63-74,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10271121)

摘　　要：研究了含分散时滞反馈的Chen系统,利用Routh-Hurwitz准则分析了在弱核及强核情形下平衡点的局部稳定性及Hopf分支的存在性．还运用规范型理论及中心流形定理,得出了包括决定分支周期解的方向、稳定性和周期的清晰的计算公式,其结果可用于混沌控制分析．Chen＇s system with distributed delays feedback is studied. After the local stability of the equilibrium is analyzed in the weak and strong kernel case by using the Routh-Hurwitz criterion, the existence of Hopf bifurcation is discussed. The explicit formulas determining the direction, stability and period of the bifurcating periodic solutions are obtained by employing the normal form theory and the center manifold theorem. The results can be used in the analysis of the control of chaos.

关 键 词：稳定性 CHEN系统 HOPF分支 

分 类 号：O175.14[理学—数学]