Stripe and Spot Patterns in a Gierer-Meinhardt Activator-Inhibitor Model with Different Sources

doi:10.1142/S0218127415501084

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	Stripe and Spot Patterns in a Gierer-Meinhardt Activator-Inhibitor Model with Different Sources
	Wang, Jinliang 1,2; Hou, Xiaojie 3; Jing, Zhujun 4
	2015-07-01
发表期刊	INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN	0218-1274
卷号	25 期号:8 页码:16
摘要	In this paper, we study the Turing patterns in a Gierer-Meinhardt model of the activator-inhibitor type with different sources. First, we investigate the corresponding kinetic equations and derive the conditions for the stability of the equilibrium and then, we turn our attention to the Hopf bifurcation of the system. In certain parameter range, the equilibrium experiences a Hopf bifurcation; the bifurcation is supercritical and the bifurcated periodic solution is stable. With added diffusions, we show that both the equilibrium and the stable Hopf periodic solution experience Turing instability, if the diffusion coefficients of the two species are sufficiently different. Our numerical simulations show that the Turing patterns are either spot or stripe type. The results are new.
关键词	Hopf bifurcation Turing instability stability spatial and temporal pattern
DOI	10.1142/S0218127415501084
语种	英语
资助项目	National Natural Science Foundation of China[10971009] ; National Natural Science Foundation of China[10771196] ; National Scholarship Fund[201303070222] ; Fundamental Research Funds for the Central Universities
WOS研究方向	Mathematics ; Science & Technology - Other Topics
WOS类目	Mathematics, Interdisciplinary Applications ; Multidisciplinary Sciences
WOS记录号	WOS:000359318000017
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20530
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Jinliang
作者单位	1.Beihang Univ, LMIB, Beijing 100191, Peoples R China 2.Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China 3.Univ N Carolina, Dept Math & Stat, Wilmington, NC 28403 USA 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang, Jinliang,Hou, Xiaojie,Jing, Zhujun. Stripe and Spot Patterns in a Gierer-Meinhardt Activator-Inhibitor Model with Different Sources[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,2015,25(8):16.
APA	Wang, Jinliang,Hou, Xiaojie,&Jing, Zhujun.(2015).Stripe and Spot Patterns in a Gierer-Meinhardt Activator-Inhibitor Model with Different Sources.INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,25(8),16.
MLA	Wang, Jinliang,et al."Stripe and Spot Patterns in a Gierer-Meinhardt Activator-Inhibitor Model with Different Sources".INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 25.8(2015):16.