中文摘要：

运用定性分析和分支理论,研究了一类含时滞与收获的Monod-Haldane型捕食系统的动力学行为,确定了Hopf分支发生时的时滞τ的临界条件,并通过规范型理论和中心流行定理,研究了Hopf分支的方向与稳定性等.最后,利用数值模拟验证了研究结果.

英文摘要：

In this paper,by using the analysis of qualitative method and bifurcation theory,we investigated the dynamics of the Monod-Haldane type predator-prey system with constant prey harvesting and a single time delay.It is shown that the Hopf bifurcation can occur as the delayτcrosses some critical values.Furthermore,the direction and stability of the Hopf bifurcation are determined by deriving normal form theory and center manifold theorem.Finally,numerical simulations are performed to illustrate the analytical results.