中文摘要：

研究了一类含时滞且含干扰和收获率的广义Logistic模型的Hopf分支周期解。得到该模型正平衡态存在唯一的充要条件,利用特征值理论得到该模型产生Hopf分支的条件;利用周期函数正交性方法得到其近似周期解的表达式;运用计算机仿真,给出了参数取不同数值时的曲线拟合图,讨论了参数对周期解的周期、振幅及正平衡态的影响。

英文摘要：

The Hopf bifurcation periodic solution of a class of general logistic model with time delay,disturb and yield rate is discussed.The necessary and sufficient condition for the existence and uniqueness of the positive equilibrium is obtained.The condition for the existence of bifurcation period solution is obtained by the Eigen value theory;the form of approximate period solution is derived by the orthogonal condition;fitted curve figures are achieved by Matlab,when parameters are assigned different values.The effect of parameters on the period,swing,and position equilibrium of the periodic solution are discussed.