Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth
Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth
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DOI：
10.1016/j.camwa.2015.08.019
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发表时间：
2015-10-01
影响因子：
2.9
通讯作者：
Sgurad, I.
中科院分区：
文献类型：
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作者：
Bozzini, B.;Gambino, G.;Sgurad, I.
我们专注于Bozzini等人（2013）引入的形态化学反应扩散模型，并进行非线性分叉分析，旨在表征物理相关平衡的图灵不稳定性导致的图案的形状和幅度。我们进行了弱非线性多尺度分析，并推导出，规范型方程的振幅模式。这些振幅方程使我们能够构建模型方程的相关解决方案，并揭示了亚临界分岔的结果所产生的稳定的解决方案的多个分支的存在。滞后型现象也突出通过数值模拟。我们展示了空间模式传播的发生，并推导出描述行波波前包络的Ginzburg-Landau方程。(C)2015爱思唯尔有限公司版权所有。
We focus on the morphochemical reaction-diffusion model introduced in Bozzini et al. (2013) and carry out a nonlinear bifurcation analysis with the aim to characterize the shape and the amplitude of the patterns arising as the result of Turing instability of the physically relevant equilibrium. We perform a weakly nonlinear multiple scales analysis, and derive, the normal form equations governing the amplitude of the patterns. These amplitude equations allow us to construct relevant solutions of the model equations and reveal the presence of multiple branches of stable solutions arising as the result of subcritical bifurcations. Hysteretic type phenomena are highlighted also through numerical simulations. We show the occurrence of spatial pattern propagation and derive the Ginzburg-Landau equation describing the envelope of the traveling wavefront. (C) 2015 Elsevier Ltd. All rights reserved.