Effects of dispersal for a predator-prey model in a heterogeneous environment

Yaying Dong; Shanbing Li; Yanling Li

doi:10.3934/cpaa.2019114

Article Contents

2019, Volume 18, Issue 5: 2511-2528. Doi: 10.3934/cpaa.2019114

This issue Previous Article Large deviations for stochastic 3D Leray-

$ \alpha $

model with fractional dissipation Next Article Global existence and asymptotic behavior of spherically symmetric solutions for the multi-dimensional infrarelativistic model

Effects of dispersal for a predator-prey model in a heterogeneous environment

1.
School of Science, Xi'an Polytechnic University, Xi'an, Shaanxi, 710048, China
2.
School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi 710071, China
3.
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China

Received: May 31, 2018

Revised: October 31, 2018

Published: March 2019

The work is supported by the Natural Science Foundation of China (11801431, 61672021), the Postdoctoral Science Foundation of China (2018T111014, 2018M631133), the Natural Science Foundation of Shaanxi Province (2018JQ1004, 2018JQ1017), Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 18JK0343)

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Abstract

In this paper, we study the stationary problem of a predator-prey cross-diffusion system with a protection zone for the prey. We first apply the bifurcation theory to establish the existence of positive stationary solutions. Furthermore, as the cross-diffusion coefficient goes to infinity, the limiting behavior of positive stationary solutions is discussed. These results implies that the large cross-diffusion has beneficial effects on the coexistence of two species. Finally, we analyze the limiting behavior of positive stationary solutions as the intrinsic growth rate of the predator species goes to infinity.

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Mathematics Subject Classification: Primary: 35J55, 92D40; Secondary: 35B30, 35B32.

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