In this paper, we consider a reaction–diffusion mussel–algae model with state-dependent mussel mortality. This mortality involves a positive feedback term resulting from the reduction of dislodgment and predation and a negative feedback term resulting from the intraspecific competition for mussel. We first study the global stability of the nonnegative uniform steady states and then focus on the existence and nonexistence of nonconstant positive steady states. The global bifurcation of constant positive steady state is also considered. Our results suggest that the regular patterning in mussel beds may be caused by the high mobility of algae or the low diffusion of mussels.

中文翻译：

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反应-扩散贻贝-藻类模型的平稳模式

在本文中，我们考虑了具有状态依赖性贻贝死亡率的反应-扩散贻贝-藻类模型。这种死亡率包括一个因移出和捕食减少而产生的正反馈项和一个因贻贝种内竞争产生的负反馈项。我们首先研究非负均匀稳态的全局稳定性，然后关注非常量正稳态的存在和不存在。还考虑了恒定正稳态的全局分叉。我们的结果表明，贻贝床中的规则图案可能是由藻类的高流动性或贻贝的低扩散引起的。