中文摘要：

通过非线性动力学理论,对时滞类Lorenz系统在平衡点的稳定性问题和发生Hopf分岔的条件进行了研究.首先计算得到系统的平衡点,然后通过分析系统在平衡点处的相应特征方程根的分布,得到系统在平衡点局部渐近稳定和产生Hopf分岔的时滞临界点.以时滞为分叉参数,研究了时滞系统存在Hopf分岔的条件.最后,利用Matlab程序进行仿真验证所得结论与理论分析一致.本文的结论是对一些已有文献研究成果的推广.

英文摘要：

In this paper,we analyze the stability and Hopf bifurcation condition of the system at its balance by using the nonlinear dynamics theory.The equilibrium point is obtained and then critical point of the delay for local stability of the equilibrium and existence of local Hopf bifurcation is also obtained by analyzing distribution of roots of the corresponding characteristic equation.the condition for the existence of Hopf bifurcation of this delay system is studied by taking delay as bifurcation parameter.Furthermore,by Matlab program some numerical simulations were given to show the correctness of the obtained conclusion.This paper extends the research achievements in the cited literature.