Turing Instability and Pattern Formation for the Lengyel–Epstein System with Nonlinear Diffusion
Turing Instability and Pattern Formation for the Lengyel–Epstein System with Nonlinear Diffusion
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DOI：
10.1007/s10440-014-9903-2
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发表时间：
2014-03
影响因子：
1.6
通讯作者：
G. Gambino;M. Lombardo;M. Sammartino
中科院分区：
文献类型：
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作者：
G. Gambino;M. Lombardo;M. Sammartino
本文研究了Lengyel-Epstein系统中密度相关非线性扩散对斑图形成的影响。通过线性稳定性分析，我们确定的图灵和霍普夫不稳定的边界，我们展示了如何非线性扩散加剧的趋势，图案的形成，特别是，与经典的线性扩散的情况下，图灵不稳定性可以发生，即使当扩散的抑制剂是显着慢于激活剂的。在图灵模式区域中，我们进行WNL多尺度分析，以推导出超临界和亚临界情况下的稳态模式的振幅方程。此外，我们计算复杂的Ginzburg-Landau方程在附近的Hopf分岔点，因为它给出了一个缓慢的时空调制的相位和振幅的均匀振荡的解决方案。
In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel–Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear diffusion intensifies the tendency to pattern formation; in particular, unlike the case of classical linear diffusion, the Turing instability can occur even when diffusion of the inhibitor is significantly slower than activator’s one. In the Turing pattern region we perform the WNL multiple scales analysis to derive the equations for the amplitude of the stationary pattern, both in the supercritical and in the subcritical case. Moreover, we compute the complex Ginzburg–Landau equation in the vicinity of the Hopf bifurcation point as it gives a slow spatio-temporal modulation of the phase and amplitude of the homogeneous oscillatory solution.