This paper analyzes prey–predator models with indirect predator-taxis in such a way that chemical secreted by the predator triggers the repellent behavior of prey against the predator. Under the assumption of quadratic decay of predator, we prove the global existence and uniform boundedness of classical solutions up to two spatial dimensions. Moreover, via the linear stability analysis, we show that large chemosensitivity gives rise to the occurrence of pattern formations. We also obtain the global stability results for the nontrivial constant steady states by establishing proper Lyapunov functionals.

中文翻译：

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带有间接捕食出租车的食饵-捕食者模型的全局可解性

本文分析了带有间接捕食者-出租车的捕食者-捕食者模型，这种方式使得捕食者分泌的化学物质触发了捕食者对捕食者的驱避行为。在捕食者呈二次衰减的假设下，我们证明了经典解在两个空间维度上的整体存在性和一致有界性。此外，通过线性稳定性分析，我们显示出较大的化学敏感性引起图案形成的发生。通过建立适当的Lyapunov泛函，我们还获得了非平凡恒定稳态的全局稳定性结果。