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

✍ Scribed by Xinyu Song; Yongfeng Li

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 695 KB
• Volume: 9
• Category: Article
• ISSN: 1468-1218
• DOI: 10.1016/j.nonrwa.2006.09.004

✦ Synopsis

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 semitrivial 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.