中文摘要：

本文考虑了一类延迟积分-微分方程的Hopf分岔分析．利用敏感性方程，确定了一个合适的Hopf参数．基于Hopf分岔理论得到，当系统存在Hopf分岔时系统参数必须满量的条件．为了得到Hopf参数的精确值，进一步讨论了延迟积分一微分方程的离散形式，利用Newton迭代法，得到了参数的逼近值．最后，数值仿真说明了我们的理论的有效性．

英文摘要：

This paper deals with Hopf bifurcation analysis of a kind of delay integro-differential equations. Applying the sensitivity equation,we determine the suitable Hopf bifurcation parameter first. Based on the theory of Hopf bifurcation,we obtain the relation of the pa- rameters when the system has a Hopf bifurcation. In order to get the exact value of the Hopf bifurcation point,we discuss the discrete version of the integro-differential equation,and use the approximation parameter as the initial value of the Newton iteration method. At last,nu- merical simulations show that our theory are reasonable.