时滞R?ssler系统的Hopf分岔分析  

Hopf Bifurcation Analysis of Time-delay R?ssler System

作　　者：赵少卿 崔岩[1] 周六圆 孙观 何宏骏 ZHAO Shaoqing;CUI Yan;ZHOU Liuyuan;SUN Guan;HE Hongjun(School of Mechanical&Automotive Engineering,Shanghai University of Engineering Science,Shanghai 201620,China)

机构地区：[1]上海工程技术大学机械与汽车工程学院

出　　处：《河南科技大学学报（自然科学版）》2020年第1期93-99,M0008,共8页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金青年项目(11604205)

摘　　要：研究了时滞Rossler系统的Hopf分岔问题。将规范形和Hopf分岔理论相结合,给出时滞Rossler系统的Hopf分岔产生条件,得出了系统时滞参量的Hopf分岔点,并分析了系统在时滞分岔点附近的稳定性。在计算过程中,采用换元法简化了在非零平衡点处的线性化系统,减少了对系统Hopf分岔分析的运算量。通过MATLAB软件绘制了系统在不同时滞参量条件下的仿真图像。仿真结果表明:时滞Rossler系统在时滞分岔点发生了超临界Hopf分岔,且时滞参量在时滞分岔点附近的改变会影响系统的稳定性。The Hopf bifurcation problem of time-delay Rossler system was studied. Combining canonical form with Hopf bifurcation theory,the occurrence condition of Hopf bifurcation of time-delay Rossler system was given.The Hopf bifurcation point of time-delay parameter of the system was obtained and the stability of the system near the time delay bifurcation point was analyzed.In the process of calculation,the substitution method was adopted to simplify the linearized system at the non-zero equilibrium point and reduce the computation of Hopf bifurcation analysis of the system. The simulation images of the system with different time-delay parameters were drawn by MATLAB software. The simulation results show that the time-delay Rossler system brings about supercritical Hopf bifurcation at the time-delay bifurcation point. The change of the time-delay parameter near the time-delay bifurcation point affects the stability of the system.

关 键 词：混沌 时滞 ROSSLER系统 HOPF分岔 

分 类 号：O415[理学—理论物理] O322[理学—物理]