具有非线性扩散的自振子系统的图灵斑图形成
Turing pattern formation in the Brusselator system with nonlinear diffusion
摘要：
在本工作中，我们研究了密度相关的非线性扩散对量子选择器系统中斑图形成的影响。通过对基本解的线性稳定性分析，确定了图灵和振荡不稳定边界。与经典的线性扩散的比较表明，如何非线性扩散有利于图灵斑图形成的发生。我们研究了斑图形成的过程中，在一维和二维空间域。通过弱非线性多尺度分析，我们推导出的平稳模式的振幅方程。振幅方程的分析表明，发生了一些不同的现象，包括稳定的超临界和亚临界图灵模式与多个分支的稳定的解决方案，导致滞后。此外，我们考虑行波图案化波：当域的大小是大的，图案的形式顺序和行波波前的前兆图案。我们推导出了Ginzburg-Landau方程，并描述了旅行前包围一个模式，侵入域。我们的径向对称目标模式的出现，并通过匹配过程中，我们构建的外部振幅方程和内核的解决方案。
英文摘要：
In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the process of pattern formation both in 1D and 2D spatial domains. Through a weakly nonlinear multiple scales analysis we derive the equations for the amplitude of the stationary patterns. The analysis of the amplitude equations shows the occurrence of a number of different phenomena, including stable supercritical and subcritical Turing patterns with multiple branches of stable solutions leading to hysteresis. Moreover we consider traveling patterning waves: when the domain size is large, the pattern forms sequentially and traveling wavefronts are the precursors to patterning. We derive the Ginzburg-Landau equation and describe the traveling front enveloping a pattern which invades the domain. We show the emergence of radially symmetric target patterns, and through a matching procedure we construct the outer amplitude equation and the inner core solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
