Abstract In this paper, we consider the optimal harvesting controls for a diffusive predator-prey system, which is formulated by prey refuge and modified Leslie-Gower functional response. The locally and globally asymptotic stability of unique positive constant steady state is discussed under homogeneous Neumann boundary condition. The nonexistence and existence of nonconstant steady states are obtained by Leray-Schauder degree theory. Also, the optimal harvesting strategies to get maximum sustainable yield (MSY) and maximum economic yield (MEY) are correspondingly given.

中文翻译：

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在包含猎物避难所的空间异质环境中，扩散捕食者-猎物系统的最优性

摘要 在本文中，我们考虑了由猎物避难所和修正的 Leslie-Gower 功能响应制定的扩散捕食者-猎物系统的最佳收获控制。讨论了齐次Neumann边界条件下唯一正常稳态的局部和全局渐近稳定性。非恒定稳态的不存在和存在是通过 Leray-Schauder 度理论得到的。此外，相应地给出了获得最大可持续产量（MSY）和最大经济产量（MEY）的最佳收获策略。