Abstract This paper is concerned with the stationary problem for a diffusive Lotka-Volterra predator-prey-mutualist model with a protection zone under homogeneous Neumann boundary conditions. Compared with the case where the mutualist is absent in [12] , this paper aims to reveal the effects of mutualism coefficients α and β on the existence, number and stability of steady states. It turns out that when α is large, the model has at most one steady state and it is stable (if it exists); however existence of multiple steady states is examined for large β, moreover asymptotic profiles of steady states are established as β tends to infinity.

中文翻译：

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具有保护区的扩散捕食者-猎物-互惠模型稳态的唯一性和非唯一性

摘要 本文研究了在齐次 Neumann 边界条件下具有保护区的扩散 Lotka-Volterra 捕食者-猎物-互助模型的平稳问题。与文献[12]中不存在互惠因子的情况相比，本文旨在揭示互惠因子α和β对稳态的存在、数量和稳定性的影响。事实证明，当α很大时，模型最多有一个稳态并且是稳定的（如果存在）；然而，当 β 趋于无穷大时，检查了多个稳态的存在性，并且建立了稳态的渐近曲线。