In this paper, we discuss a diffusive predator‐prey model with predator cannibalism in spatially heterogeneous environments. In contrast with spatially homogeneous environments, we find the dynamics of the model in spatially heterogenous environments is more complicated. For the spatially heterogeneous case, we could classify death rate of the predator into four different regions and demonstrate that for every region, this model with Neumann boundary conditions has at least one positive steady state for some ranges of dispersal rates of the predator and prey via Leray–Schauder degree theory. In particular, for some scopes of death rate of the predator, this model has multiple positive steady states for certain ranges of dispersal rates of the predator and prey.

中文翻译：

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空间异质环境中扩散捕食者－食饵模型的多个正稳态

在本文中，我们讨论了在空间异质环境中具有食肉食人主义的扩散捕食者－食饵模型。与空间同质环境相比，我们发现模型在空间异质环境中的动力学更为复杂。对于空间异构情况，我们可以将捕食者的死亡率划分为四个不同的区域，并证明对于每个区域，具有Neumann边界条件的该模型对于捕食者和被捕食者的某些扩散率范围均具有至少一个正稳态。 Leray-Schauder学位理论。特别地，对于捕食者的某些死亡率范围，该模型对于捕食者和猎物的某些扩散率范围具有多个正稳态。