Dynamic behaviors of the periodic predator–prey model with modified Leslie-Gower Holling-type II schemes and impulsive effect |
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Institution: | 1. Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan, PR China;2. School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, Jiangsu, PR China |
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Abstract: | 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. |
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