交叉扩散对模式形成的影响

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-10-08 DOI:10.3934/JCD.2021010

M. Breden, C. Kuehn, C. Soresina

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引用次数: 13

摘要

本文考虑了Shigesada-Kawasaki-Teramoto (SKT)模型来解释表现空间分离的稳定非均匀稳态，这描述了两个竞争物种共存的情况。我们通过延拓软件pde2path将详细的线性化分析与先进的数值分岔方法相结合，对非齐次稳态存在的交叉扩散和反应系数的条件有了更深入的了解。我们报告了一些数值实验，表明当考虑交叉扩散时，在共存均匀稳态为正的参数范围之外存在正稳定的非均匀稳态。此外，我们还分析了考虑自扩散项的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the influence of cross-diffusion in pattern formation

In this paper we consider the Shigesada-Kawasaki-Teramoto (SKT) model to account for stable inhomogeneous steady states exhibiting spatial segregation, which describe a situation of coexistence of two competing species. We provide a deeper understanding on the conditions required on both the cross-diffusion and the reaction coefficients for non-homogeneous steady states to exist, by combining a detailed linearized analysis with advanced numerical bifurcation methods via the continuation software pde2path. We report some numerical experiments suggesting that, when cross-diffusion is taken into account, there exist positive and stable non-homogeneous steady states outside of the range of parameters for which the coexistence homogeneous steady state is positive. Furthermore, we also analyze the case in which self-diffusion terms are considered.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.