一类具有时滞和Holling Ⅱ型功能反应的捕食模型的全局稳定性和分支（英文）

Global stability and bifurcation of a delayed predatorprey model with Holling type Ⅱ functional response

研究一类考虑捕食者妊娠产生的时滞和Holling II功能性反应的两种群捕食模型。通过分析特征方程,研究模型可行平衡点的局部稳定性及共存平衡点处Hopf分支的存在性。使用无穷维系统的持久性理论,证明当共存平衡点存在时,模型的持久性。通过构造恰当的李雅普诺夫函数以及使用La Salle不变性原理,证明当共存平衡点不存在时,捕食者灭绝平衡点是全局渐近稳定的;给出共存平衡点全局渐近稳定的充分条件。数值模拟例子验证了理论结果。

A two-species predator-prey system with Holling type II functional response and time delay due to the gestation of the predator is investigated. By analyzing the characteristic equations, the local stabili- ty of each of feasible equilibria of the system is studied and the existence of a Hopf bifurcation at the co- existence equilibrium is established. By using the persistence theory on infinite dimensional systems, it is shown that the system is permanent provided that the coexistence equilibrium exists. By means of novel Lyapunov functionals and LaSalle＇ s invariant principle, it is proven that the predator-extinction equilibri- um is globally asymptotically stable when the coexistence equilibrium is not feasible; and sufficient condi- tions are obtained for the global asymptotic stability of the coexistence equilibrium. Numerical simulations are carried out to illustrate the main theoretical results.