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

Baek, Hun-Ki;Jung, Chang-Do

  • Received : 2009.11.15
  • Accepted : 2009.12.16
  • Published : 2009.12.31

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

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Cited by

  1. Complex Dynamic Behaviors of an Impulsively Controlled Predator-prey System with Watt-type Functional Response vol.56, pp.3, 2016, https://doi.org/10.5666/KMJ.2016.56.3.831
  2. On the Dynamical Behavior of a Two-Prey One-Predator System with Two-Type Functional Responses vol.53, pp.4, 2013, https://doi.org/10.5666/KMJ.2013.53.4.647