Existence of Turing instabilities in a two-species fractional reaction-diffusion system
Existence of Turing instabilities in a two-species fractional reaction-diffusion system
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DOI：
10.1137/s0036139900375227
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发表时间：
2002-02-21
影响因子：
1.9
通讯作者：
Wearne, SL
中科院分区：
文献类型：
--
作者：
Henry, BI;Wearne, SL
我们引入一个两种群分数阶反应扩散系统来模拟空间非均匀介质中具有反常扩散的活化剂-抑制剂动力学。图灵不稳定性诱导图案形成的条件推导出这些分数激活剂-抑制剂系统，从而均匀的稳态解是稳定的，在没有扩散，但变得不稳定的波数范围时，分数扩散存在。的条件被施加到一个变种的Gierer-Meinhardt反应动力学已被推广到将异常扩散中的一个或两个的激活剂和抑制剂变量。反常扩散扩大了扩散系数的范围，在此范围内可以出现图灵图样。这个分析提出了一个有趣的可能性，当激活剂的扩散是异常的，但抑制剂的扩散是有规律的，这可能会出现，即使当激活剂的扩散系数超过抑制剂的扩散系数时，图灵不稳定性也可能存在。
W introduce a two-species fractional reaction-diffusion system to model activator-inhibitor dynamics with anomalous diffusion such as occurs in spatially inhomogeneous media. Conditions are derived for Turing-instability induced pattern formation in these fractional activator-inhibitor systems whereby the homogeneous steady state solution is stable in the absence of diffusion but becomes unstable over a range of wavenumbers when fractional diffusion is present. The conditions are applied to a variant of the Gierer-Meinhardt reaction kinetics which has been generalized to incorporate anomalous diffusion in one or both of the activator and inhibitor variables. The anomalous diffusion extends the range of diffusion coefficients over which Turing patterns can occur. An intriguing possibility suggested by this analysis, which can arise when the diffusion of the activator is anomalous but the diffusion of the inhibitor is regular, is that Turing instabilities can exist even when the diffusion coefficient of the activator exceeds that of the inhibitor.