SIAM Review, Volume 64, Issue 3, Page 728-747, August 2022.
The Gray--Scott model is a widely studied autocatalytic model that exhibits a range of interesting pattern formation behavior, as well as a rich structure of dynamics that includes many ideas from a typical undergraduate dynamical systems course, and some from beyond. Gaining an understanding of the solutions to this model is arguably most easily conducted via a bifurcation analysis of corresponding ODE problems within the software XPPAUT. In this paper, we provide an introductory XPPAUT tutorial, through which we begin to expose the range of intricate patterns that the Gray--Scott model emits.

中文翻译：

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分析灰色模式的形成--斯科特模型：XPPAUT 教程

SIAM 评论，第 64 卷，第 3 期，第 728-747 页，2022
年 8 月。Gray-Scott 模型是一种广泛研究的自催化模型，展示了一系列有趣的模式形成行为，以及丰富的动力学结构，包括许多来自典型的本科动力系统课程的想法，以及一些来自其他课程的想法。可以说，通过对 XPPAUT 软件中相应 ODE 问题的分叉分析，最容易理解该模型的解决方案。在本文中，我们提供了一个介绍性的 XPPAUT 教程，通过它我们开始揭示 Gray-Scott 模型发出的复杂模式的范围。