Turing pattern formation with fractional diffusion and fractional reactions
Turing pattern formation with fractional diffusion and fractional reactions
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DOI：
10.1088/0953-8984/19/6/065115
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发表时间：
2007-01
期刊：
影响因子：
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通讯作者：
T. Langlands;B. Henry;S. Wearne
中科院分区：
文献类型：
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作者：
T. Langlands;B. Henry;S. Wearne
我们通过线性稳定性分析和数值模拟研究了两种群反应扩散系统中图灵图案的形成，其中分数阶时间导数作用于两种群以及扩散项和反应项。分数导数的阶数影响图案化开始的时间，但不影响图灵不稳定性开始的临界参数，也不影响最终的空间图案化。这些结果与以前关于分数阶反应扩散系统中图灵图的形成的研究相反，扩散项上有分数阶时间导数，而反应项上没有分数阶时间导数。除了阐明这两个模型系统之间的差异外，我们的研究还提供了进一步的证据，证明图灵线性不稳定性分析是预测分数阶非线性反应扩散方程中模式形成的开始和性质的一个很好的因子。
We have investigated Turing pattern formation through linear stability analysis and numerical simulations in a two-species reaction–diffusion system in which a fractional order temporal derivative operates on both species, and on both the diffusion term and the reaction term. The order of the fractional derivative affects the time onset of patterning in this model system but it does not affect critical parameters for the onset of Turing instabilities and it does not affect the final spatial pattern. These results contrast with earlier studies of Turing pattern formation in fractional reaction–diffusion systems with a fractional order temporal derivative on the diffusion term but not the reaction term. In addition to elucidating differences between these two model systems, our studies provide further evidence that Turing linear instability analysis is an excellent predictor of both the onset of and the nature of pattern formation in fractional nonlinear reaction–diffusion equations.