文章基本信息

标题：Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System
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作者：Qianiqian Zheng ; Zhijie Wang ; Jianwei Shen 等
期刊名称：Advances in Mathematical Physics
印刷版ISSN：1687-9120
电子版ISSN：1687-9139
出版年度：2017
卷号：2017
DOI：10.1155/2017/9648538
出版社：Hindawi Publishing Corporation
摘要：Noise is ubiquitous in a system and can induce some spontaneous pattern formations on a spatially homogeneous domain. In comparison to the Reaction-Diffusion System (RDS), Stochastic Reaction-Diffusion System (SRDS) is more complex and it is very difficult to deal with the noise function. In this paper, we have presented a method to solve it and obtained the conditions of how the Turing bifurcation and Hopf bifurcation arise through linear stability analysis of local equilibrium. In addition, we have developed the amplitude equation with a pair of wave vector by using Taylor series expansion, multiscaling, and further expansion in powers of small parameter. Our analysis facilitates finding regions of bifurcations and understanding the pattern formation mechanism of SRDS. Finally, the simulation shows that the analytical results agree with numerical simulation.