交叉扩散对模式形成的影响

IF 1 Q3 Engineering

Journal of Computational Dynamics 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

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.