一个新混沌系统的Hopf分岔分析及其电路实现  

An analysis of hopf bifurcation and circuit experiment simulation for a new chaotic system

作　　者：杜文举[1] 俞建宁[1] 张建刚[1] 安新磊[1] 

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《四川大学学报（自然科学版）》2013年第5期1025-1031,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11161027);教育部科技研究重点项目(212180);甘肃省自然科学基金(101RJZA067)

摘　　要：通过非线性动力学理论,分析了一个混沌系统的平衡点的稳定性,对该系统的平衡点进行了Hopf分岔分析,得出Hopf分岔的参数条件.经过计算系统在平衡点的第一Lyapunov系数判断了分岔的方向及其稳定性.最后进行了仿真模拟与实际电路的设计,实验结果与理论推导吻合.In this paper, a new chaotic system is studied More precisely, we study the stability of the equilibrium in detail by varying three control parameters. points and basic dynamic properties of the au tonomous system by means of nonlinear dynamics theory. The existence of Hopf bifurcation is investiga ted by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direc tion of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Then, a nu merical example is given. Finally, the oscillator circuit of the new chaotic system is designed.

关 键 词：混沌系统 LYAPUNOV指数 POINCARÉ截面 HOPF分岔 电路仿真 

分 类 号：O415.5[理学—理论物理]