一类具时滞的人机系统的Hopf分支分析  

Hopf bifurcation analysis of man-machine system involving time delays

作　　者：王洪滨[1] 高晓艳[1] 

机构地区：[1]哈尔滨工业大学数学系

出　　处：《哈尔滨工业大学学报》2008年第11期1789-1792,共4页Journal of Harbin Institute of Technology

基　　金：国家自然科学基金资助项目(10771045);黑龙江省自然科学基金(A200806);哈尔滨工业大学理学研究基金资助项目(HITC200707)

摘　　要：研究了控制力中时滞对人机系统的Hopf分支性质的影响,通过对系统的线性化的特征方程的分析,发现当时滞经过某临界值时系统会产生Hopf分支.利用规范型理论和中心流形定理给出了关于分支周期解的稳定性及Hopf分支方向的计算公式,数值模拟与理论分析结果具有一致性.可见,通过调整时滞的大小可以实现对系统动力学行为的控制.To discuss the effects of change of time delay on the dynamics of a nonlinear system, the Hopf bifurcation analyses on the role played by the delay in the control force of a structurally unstable man-machine system were investigated. By analyzing the associated characteristic equation, it is found that the Hopf bifurcation occurs when the delay passes through a critical value. The explicit algorithm for determining the direction of the Hopf bifurcation and the stability of bifurcated periodic solutions were derived using the theory of normal form and center manifold. Results of numerical simulations agree well with the theoretical analysis results, which means that the system control can be realized by adjusting the magnitude of time delay.

关 键 词：人机系统 时滞 稳定性 HOPF分支 

分 类 号：O175.13[理学—数学]