一类含有随机参数的混沌系统的Hopf分岔研究  

Hopf bifurcation study of a class of chaotic systems containing random parameter

作　　者：殷俊[1] 张建刚[1] 南娟[1] 卢加荣 庞琴[1] 

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《重庆文理学院学报（社会科学版）》2016年第5期29-33,共5页Journal of Chongqing University of Arts and Sciences（Social Sciences Edition)

摘　　要：文章选取随机变量为系统的随机变量研究含有随机参数混沌系统的Hopf分岔,利用Chebyshev正交多项式逼近理论将含有随机变量的系统转化为等价的确定性系统,通过Hopf分岔定理和Lyapunov系数讨论了随机参数系统的Hopf分岔及稳定性,发现随机系统的渐进稳定性参数区间大小不仅和确定性参数有关,还与随机参数有非常密切的关系.In the paper the random parameter was used to study the Hopf bifurcation of chaotic system contai-ning random parameter, and the Chebyshev polynomial approximation theory was used to change the system containing random parameter into the deterministic equivalent system. Through the Hopf bifurcation theory and Lyapunov coefficient to discuss the Hopf bifurcation and stability of random stochastic parameter system, it shows that the critical value of stochastic Hopf bifurcation is determined not only by deterministic parame-ters in stochastic system, but also by the intensity of random parameter.

关 键 词：随机Hopf分岔 Chebyshev正交多项式逼近 稳定性 

分 类 号：O21[理学—概率论与数理统计]