Multiple Periodicity in a Predator–Prey Model with Prey Refuge

Weijie Lu,Yonghui Xia

doi:10.3390/math10030421

Abstract

We consider a delayed prey–predator model incorporating a refuge with a non-monotone functional response. It is supposed that prey can live in the predatory region and prey refuge, respectively. Based on Mawhin’s coincidence degree and nontrivial estimation techniques for a priori bounds of unknown solutions to the operator equation Lv=λNv, we prove the existence of multiple periodic solutions. Finally, an example demonstrates the feasibility of our main results.

Highlights

The predator–prey model [1,2] generally takes the form of dxi(t) dt = xi(t)[ri(t) + n∑ aijxj(t)], j=1 i = 1, 2, · · ·, n.Citation: Lu, W.; Xia, Y
A delayed prey–predator model incorporating a refuge with a nonmonotone functional response is considered
It is assumed that prey can live in the predatory region and the prey refuge, respectively

Summary

Introduction

When in a high-prey refuge ecological system, Sahoo et al [27,28] observed that the possibility of predator extinction could be eliminated by providing additional food to the predator population. Motivated by these works, Jana et al [29] considered the following prey–predator model with prey refuge: du dt dv dt dw dt. Motivated by the works of Jana et al [29] and Chen [34], in the present paper, we establish the following delayed stage-structured prey–predator model with a prey refuge and non-monotone functional response: dx dt r1(t)x(t)(1 −.

The Existence of Multiple Positive Periodic Solutions

Conclusions