In this paper, we show the global boundedness and stability of solutions for prey-taxis model with handling and searching predators in a two-dimensional bounded domain with smooth boundary. First, entropy-like equations and boundedness criteria are derived, and it is proved that the system has a unique uniformly bounded global classical solution. In addition, we show that prey-only steady state is globally asymptotically stable if the predator is weak. The convergence rate of solutions to the steady states is derived in the paper.

中文翻译：

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带有处理和搜索捕食者的食饵出租车模型解决方案的全局有界性和稳定性

在本文中，我们展示了在带有光滑边界的二维有界域中处理和搜索捕食者的食饵-出租车模型解的整体有界性和稳定性。首先，推导了类熵方程和有界性准则，证明了该系统具有唯一的一致有界全局经典解。另外，我们证明了如果捕食者是弱的，则只有猎物的稳态是全局渐近稳定的。推导了稳态解的收敛速度。