Turing instability of anomalous reaction–anomalous diffusion systems
Turing instability of anomalous reaction–anomalous diffusion systems
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DOI：
10.1017/s0956792508007389
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发表时间：
2008-06
影响因子：
1.9
通讯作者：
Y. Nec;A. Nepomnyashchy
中科院分区：
文献类型：
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作者：
Y. Nec;A. Nepomnyashchy
线性稳定性理论是针对激活剂-抑制剂模型而开发的，其中通常不同指数的分数阶导数算子同时作用于扩散项和反应项。结果表明，在短波极限下，对于不同物种的不同异常指数，增长率是具有解耦时间尺度的波数的幂律。在反常指数相等的情况下，得到了反应物扩散系数比反常临界值的精确公式。
Linear stability theory is developed for an activator–inhibitor model where fractional derivative operators of generally different exponents act both on diffusion and reaction terms. It is shown that in the short wave limit the growth rate is a power law of the wave number with decoupled time scales for distinct anomaly exponents of the different species. With equal anomaly exponents an exact formula for the anomalous critical value of reactants diffusion coefficients' ratio is obtained.