Pattern formation for a two-dimensional reaction-diffusion model with chemotaxis

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:475

Article

Ma, Manjun¹  Gao, Meiyan²  Carretero-Gonzalez, R.^3,4,5 

[1] Zhejiang Sci Tech Univ, Sch Sci, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

[2] China Jiliang Univ, Coll Sci, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

[3] Nonlinear Dynam Syst Grp, San Diego, CA USA

[4] Computat Sci Res Ctr, San Diego, CA USA

[5] San Diego State Univ, Dept Math & Stat, San Diego, CA 92182 USA

关键词: Pattern formation;    Amplitude equation;    Chemotaxis;    Weakly nonlinear analysis;   

DOI  :  10.1016/j.jmaa.2019.03.060

来源: Elsevier

【 摘 要 】

This paper is devoted to study the formation of stationary patterns for a chemotaxis model with nonlinear diffusion and volume-filling effect over a bounded rectangular domain. By using linear stability analysis around the homogeneous steady states we establish conditions for the existence of unstable mode bands that lead to the formation of spatial patterns. We derive the Stuart-Landau equations for the pattern amplitudes by means of weakly nonlinear multiple scales analysis and Fredholm theory. In particular, we find asymptotic expressions for a wide range of patterns sustained by the system. These patterns include mixed-mode, square, hexagonal, and roll stationary configurations. Our analytical results are corroborated by direct simulations of the underlying chemotaxis system. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free