Optimality for a diffusive predator-prey system in a spatially heterogeneous environment incorporating a prey refuge

作者：

Highlights：

• A diffusive predator-prey system in a spatially heterogeneous environment incorporating a prey refuge is proposed.

• The locally and globally asymptotic stability of unique positive constant steady state is discussed under homogeneous Neumann boundary condition.

• The existence and nonexistence of nonconstant steady states are obtained by Leray-Schauder degree theory.

• Optimal harvesting strategy for maximum sustainable yield (MSY) and maximum economic yield (MEY) are obtained.

摘要

•A diffusive predator-prey system in a spatially heterogeneous environment incorporating a prey refuge is proposed.•The locally and globally asymptotic stability of unique positive constant steady state is discussed under homogeneous Neumann boundary condition.•The existence and nonexistence of nonconstant steady states are obtained by Leray-Schauder degree theory.•Optimal harvesting strategy for maximum sustainable yield (MSY) and maximum economic yield (MEY) are obtained.

论文关键词：Predator-prey system,Diffusion,Optimality,Stability,Refuge

论文评审过程：Received 25 December 2019, Revised 15 April 2020, Accepted 17 May 2020, Available online 1 June 2020, Version of Record 1 June 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125385