Kybernetika 54 no. 3, 522-541, 2018

The dynamic behaviors of a new impulsive predator prey model with impulsive control at different fixed moments

Lin Jun Wang, You Xiang Xie and Qi Cheng DengDOI: 10.14736/kyb-2018-3-0522

Abstract:

In this paper, we propose a new impulsive predator prey model with impulsive control at different fixed moments and analyze its interesting dynamic behaviors. Sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the present model are obtained by Floquet theory of impulsive differential equation and small amplitude perturbation skills. Existences of the ``infection-free" periodic solution and the ``predator-free" solution are analyzed by bifurcation theory of impulsive differential equation. Finally, the analytical results presented in the work are validated by numerical simulation figures for this proposed model.

Keywords:

stability, impulsive control, impulsive differential equation, bifurcation theory, persistence and extinction

Classification:

34D23, 92D30

paper.pdf

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