Analysis of a predator-prey model with impulsive diffusion and releasing on predator population

Airen Zhou,Pairote Sattayatham,Jianjun Jiao

doi:10.1186/s13662-016-0834-2

Abstract

In this paper, we establish a predator-prey model with impulsive diffusion and releasing on predator population. This predator-prey model for two regions, which are connected by diffusion of predator population, portrays the evolvement of population. We prove that all solutions of the investigated system are uniformly ultimately bounded. We also prove that there exists globally asymptotically stable prey-extinction boundary periodic solution. The condition for permanence is obtained. Simulations are also employed to verify our results. It is discovered that the increasing diffusive rate of predator population will count against the pest management. We conclude that the impulsive diffusion and releasing predator provide reliable tactic basis for pest management.

Highlights

The warfare between human and pests has sustained for thousands of years
A great number of pesticides were used to control pests, the insect pests impairing crops are increasing for the resistance to pesticides
We investigate a predator-prey model with impulsive diffusion and releasing on predator population

Summary

Introduction

The warfare between human and pests has sustained for thousands of years. In the past few decades, man have adopted some advanced and modern weapons for instance chemical pesticides, biological pesticides, remote sensing and measure, computers, atomic energy, et cetera. Biological control [ – ] is one of the reduction in pest populations from the actions of other living organisms, often called natural enemies or beneficial species. (i = , ), the prey-extinction boundary periodic solution ( , y (t), , y (t)) of ( ) is globally asymptotically stable, where y∗i (i = , ) and y∗i ∗ (i = , ) are defined by ( ) and ( ). Proof First, we prove the local stability of the prey-extinction boundary periodic solution ( , y (t), , y (t)) of ( ).

Simulation analysis and discussion

The dynamical behaviors influenced by parameters μ1 and μ2