Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System
Joint Authors
Shen, Jianwei
Wang, Zhijie
Zheng, Qianqian
Iqbal, Hussain Muhammad Ather
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-02-12
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Zheng, Qianqian& Wang, Zhijie& Shen, Jianwei& Iqbal, Hussain Muhammad Ather. 2017. Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1123357
Modern Language Association (MLA)
Zheng, Qianqian…[et al.]. Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System. Advances in Mathematical Physics No. 2017 (2017), pp.1-9.
https://search.emarefa.net/detail/BIM-1123357
American Medical Association (AMA)
Zheng, Qianqian& Wang, Zhijie& Shen, Jianwei& Iqbal, Hussain Muhammad Ather. Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1123357
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123357