时滞Lorenz-like系统的Hopf分岔研究

Research on Hopf Bifurcation of Lorenz-like Delay System

随动力系统学的发展,平衡点的稳定性以及Hopf分岔对于动力系统学研究愈显重要。首先研究时滞Lorenz-like系统存在平衡点的条件,在此条件下,通过分析系统在平衡点处的线性化系统特征根的分布情况,得出系统在平衡点处的稳定性;随着系统时滞参数的变化,时滞系统在平衡点处稳定性相应地会发生改变;以时滞为分岔参数,研究了时滞系统存在Hopf分岔的条件;最后利用Matlab程序进行仿真,验证了理论分析的正确性。

With the development of power system,the stability of the equilibrium point and Hopf bifurcation are more and more important to the research on power system. This paper at first studies the condition for the equilibrium point existence in Lorenz-like delay system. Under this condition,the stability of the system at the equilibrium point is obtained by the analysis of the characteristic root distribution of the linearized system at the equilibrium point of the system. With the changing of delay parameters of the system,the stability of the delay system at the equilibrium point can change corresponding,and the condition for the existence of Hopf bifurcation of this delay system is studied by taking delay as bifurcation parameter. Finally the simulation by Matalb program tests the validity of the theoretical analysis.