一类具阶段结构和比率依赖功能性反应滞后捕食模型的稳定性和Hopf分支

Stability and Hopf Bifurcation of a Delayed Predator-Prey System with Stage Structure and Ratio-Dependent Functional Response

研究一类具阶段结构和比率依赖功能性反应的滞后捕食模型.通过分析特征方程,讨论了系统各个可行平衡点的局部稳定性,得到了系统Hopf分支存在的充分条件;利用单调迭代法和比较定理分别得到了正平衡点全局吸引和边界平衡点全局渐近稳定的充分条件.

A delayed predator-prey system with stage structure and ratio-dependent functional response is discussed.By analyzing the characteristic equations,the local stability of each of feasible equilibrium of the system is studied.The existence of Hopf bifurcation at the positive equilibrium is established.By using an iteration technique,sufficient conditions are derived for the global attraction of the positive equilibrium.By comparison arguments,sufficient conditions are obtained for the global stability of the boundary equilibrium.