中文摘要：

讨论了一类具有连续时滞的Lasota-Wazewska模型的Hopf-分支．利用特征值和分支理论，给出了与该模型的正平衡态相应的一次线性齐次近似系统的特征方程具有一对纯虚根时，给参数一个小扰动，非齐次系统分支周期解存在的条件．利用解的正交性条件，得到了分支周期解的近似解析表达式．

英文摘要：

The Hopf-bifurcation of a Lasota-Wazewska-type Model with contributed delays is investigated. The first order linear approximate system corresponding to the positive equilibrium are given. The sufficient conditions for the existence of bifurcating periodic solution is given when the characteristic equation of the linear system possesses a pair of purely imaginary roots and the parameter possesses a disturb, by using the theory about stabihty and bifurcation. The expression of the approximate periodic solution is derived, by using the solvability conditions.