一个具有唯一鞍焦点的三维混沌系统分析  

Analysis of a 3D Chaotic System with Only One Saddle Foci Equilibrium

作　　者：张康明[1] 

机构地区：[1]南昌陆军学院科文教研室

出　　处：《数学的实践与认识》2010年第14期197-202,共6页Mathematics in Practice and Theory

摘　　要：讨论了一个具有唯一鞍焦点的多参数三维混沌系统，该系统包含了Sprott提出的一个最简混沌模型．在特定的条件下得到了Hopf分岔的存在性条件；进一步利用规范型理论获得了决定Hopf分岔方向和分支周期解稳定性的公式，同时利用计算机模拟证实本文的理论分析结果．In this paper, a 3D chaotic system with multi-parameters and only one saddle loci equilibrium is investigated, which contains one of the simplest systems construsted by Sprott. We prove the existence of the Hopf bifurcation under some particular conditions. By means of normal form theory, we obtain a formula for determining the direction of the Hopf bifurcation and the stability of bifurcating period solutions. Meanwhile, numerical simulations are performed to justify theoretical analysis.

关 键 词：稳定性 HOPF分岔 混沌 

分 类 号：O415.5[理学—理论物理]