具有线性脉冲的周期捕食系统的持久性

Permanence in a periodic predator-prey system with linear impulsive perturbations

研究具有Holling IV功能性反应和脉冲的周期捕食食饵系统.找到了影响该系统动力学行为的阈值R0.证明了当R0<1时,该系统的食饵灭绝周期解是局部渐近稳定的;当R0>1时,该系统的食饵灭绝周期解变得不稳定且食饵将一致持久.

In this paper, a non-autonomous periodic predator-prey system with Holling IV functional response and impulsive perturbation is considered. The threshold value R0 which determines the dynamical behavior of the model is provided. Furthermore, we prove that the prey-eradication periodic solution is locally asymptotically stable provided R0 〈 1, the prey-eradication periodic solution is unstable and the pest will be uniform persistent when Ro 〉 1.