In this paper, we consider the new version of the Turing model proposed by Kondo (2017), which is called the kernel-based Turing model. The main aim is to study the sharp changes of interaction between local and nonlocal on the solutions of Turing model. Our results reveal that the kernel (or nonlocal) makes a key effect on the long time behavior of evolution equation, where the stable patterns appear in the diffusive nonlocal Kondo model.

中文翻译：

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基于内核的图灵模型中的非局部效应

在本文中，我们考虑了 Kondo (2017) 提出的新版图灵模型，称为基于内核的图灵模型。主要目的是研究局部和非局部相互作用对图灵模型解的急剧变化。我们的结果表明，核（或非局部）对演化方程的长期行为产生关键影响，其中稳定模式出现在扩散非局部 Kondo 模型中。