一类带有选择性收获和避难所的捕食系统的Hopf分支

Hopf Bifurcation of a Predator-prey System with Selective Harvesting and Prey Refuge

通过考虑融合食饵避难的Holling Ⅱ型功能反应函数,构造了一类捕食种群具有选择性收获的捕食-食饵系统.以收获项中的时滞为参数,利用分支理论获得了系统在正平衡点处历经Hopf分支的充分条件,并利用正规化理论和中心流形定理研究了Hopf分支的方向及分支所得周期解的稳定性.

By considering the Holling type II functional response function incorporating refuge, a predator-prey system with selecting harvesting in prey is constructed. Choosing the delay in the harvesting term as a parameter and applying the bifurcation theofy, some sufficient conditions of Hopf bifurcation at positive equilibrium of the system is studied. Based on the normal form and the center manifold theory, the direction of Hopf bifurcations and the stability of bifurcating periodic solutions are investigated.