Turing pattern formation in anisotropic medium
Turing pattern formation in anisotropic medium
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DOI：
10.1007/s10910-016-0709-5
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发表时间：
2017-03-01
影响因子：
1.7
通讯作者：
Das, Debojyoti
中科院分区：
文献类型：
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作者：
Das, Debojyoti
化学和生化系统中各向异性介质中反应物质的扩散与各向同性介质中发生的扩散明显不同，因此将扩散系数近似为常数可能不可取，因为这会产生动力学后果。本文致力于这种系统中空间模式发展的分析和数值研究。为此，我们考虑了具有浓度依赖扩散的一般反应扩散系统，并给出了导出该系统包络方程一般形式的格式。该理论应用于氯酸盐-碘化物-丙二酸体系，活化剂-抑制剂机制的标准范例，根据各向异性参数（赋予扩散系数浓度依赖性）推导不稳定条件，并在分岔图中识别超临界和亚临界图灵区。理论预测结果与数值模拟结果吻合较好。
Diffusion of reacting species in chemical and biochemical systems in anisotropic medium is markedly different from those occurring in isotropic medium, therefore approximating diffusion coefficients as constants may not be desirable as this has dynamical consequences. This paper is devoted to the analytical and numerical investigation of the development of spatial patterns in such systems. To this end we consider a general reaction-diffusion system with concentration-dependent diffusion and formulate a scheme to derive the general form of envelope equation for such systems. The theory is applied to the chlorite-iodide-malonic acid system, a standard paradigm for activator-inhibitor mechanism, to derive the instability condition in terms of the anisotropy parameters ( that impart concentration-dependence to the diffusion coefficients) and identify the supercritical and subcritical Turing regions in the bifurcation diagram. The theoretical predictions are in good agreement with the numerical simulations.