Dynamic behaviors of the periodic predator-prey model with modified Leslie-Gower Holling-type II schemes and impulsive effect

作者：Song Xinyu^*; Li Yongfeng

来源：Nonlinear Analysis: Real World Applications , 2008, 9(1): 64-79.

DOI：10.1016/j.nonrwa.2006.09.004

• Leslie-Gower
• Holling-type II
• predator-prey system
• impulsive effect
• bifurcation

In this paper, a predator-prey system which based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with impulsive effect are investigated, where all the parameters of the system are time-dependent periodic functions. By using Floquet theory of linear periodic impulsive equation, some conditions for the linear stability of trivial periodic solution and semi-trivial periodic solutions are obtained. It is proved that the system can be permanent if all the trivial and semi-trivial periodic solutions are linearly unstable. We use standard bifurcation theory to show the existence of nontrivial periodic solutions which arise near the semi-trivial periodic solution. As an application, we also examine some special case of the system to confirm our main results.

• 出版日期2008-2
• 单位信阳师范学院