Extinction and Permanence of a Holling I Type Impulsive Predator-prey Model

- Journal title : Kyungpook mathematical journal
- Volume 49, Issue 4, 2009, pp.763-770
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2009.49.4.763

Title & Authors

Extinction and Permanence of a Holling I Type Impulsive Predator-prey Model

Baek, Hun-Ki; Jung, Chang-Do;

Baek, Hun-Ki; Jung, Chang-Do;

Abstract

We investigate the dynamical properties of a Holling type I predator-prey model, which harvests both prey and predator and stock predator impulsively. By using the Floquet theory and small amplitude perturbation method we prove that there exists a stable prey-extermination solution when the impulsive period is less than some critical value, which implies that the model could be extinct under some conditions. Moreover, we give a sufficient condition for the permanence of the model.

Keywords

Predator-prey model;Holling I type functional response;impulsive differential equation;extinction;permanence;

Language

English

Cited by

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