Impulsive predator-prey model

V Volpert,Mohamed Helal,Abdelkader Lakmeche,Fayssal Charif,A Lakmeche

doi:10.1051/itmconf/20150401008

Abstract

In this paper we considered a predator-prey model with state-dependent impulse. We determine periodic solutions for the model without impulses and we prove the existence of nontrivial periodic solution in the case of impulse depending on the state of the model.

Highlights

In this work we consider a prey-predator model with impulse effects depending on the state of the model.The impulsive differential equations appear generally in the description of phenomena submitting jumps in the state variables for short time, these big changes are modeled by discrete equations called impulse effects.In this work, we consider a model inspired from [4] where two populations of insects denoted by x and y, respectively, are treated by chemical spray
The evolution of the two populations is governed by a predator-prey model and the effect of the chemical spray is described by impulse effects
In this work we have studied the stability of some periodic solutions of an impulsive prey-predator model

Summary

Introduction

In this work we consider a prey-predator model with impulse effects depending on the state of the model. The evolution of the two populations is governed by a predator-prey model and the effect of the chemical spray is described by impulse effects. Y = −qy, x = h2, where x and y represent the population densities at time t, the parameters a, b, , h and d are positive constants and p, q ∈ (0, 1).

Analysis of the model without impulses

The model with impulse effects

Conclusion