研究了一类具有两个不同时滞的捕食-食饵恒化器模型, 其中功能反应函数采用~Monod型. 应用时滞微分方程的特征方程理论对模型进行分析, 得到了系统边界平衡点稳定和不稳定的充分条件. 对于两个不同时滞对系统正平衡点的影响, 利用稳定性开关理论和分支理论, 得到了时滞变化时系统发生 稳定开关和出现hopf分支的充分条件. 最后, 通过数值模拟对文中主要结论进行了验证.

In this paper, we discuss a predator-prey model with two different delays in the chemostat. The consumption terms take the Monod type response functions. By analyzing the characteristic equations of delay differential equations, we obtain the sufficient conditions of stability of boundary equilibria. About the effect of delay on stability of the positive equilibrium, using stability switch theory and bifurcation theory, we give the sufficient conditions of appearance of stability switches and Hopf bifurcations in the delay equations as a result of changing the delay. Finally, numerical simulations are carried out to illustrate the theoretical results.