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Stripe and Spot Patterns in a Gierer-Meinhardt Activator-Inhibitor Model with Different Sources
Wang, Jinliang1,2; Hou, Xiaojie3; Jing, Zhujun4
2015-07-01
Source PublicationINTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN0218-1274
Volume25Issue:8Pages:16
AbstractIn 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.
KeywordHopf bifurcation Turing instability stability spatial and temporal pattern
DOI10.1142/S0218127415501084
Language英语
Funding ProjectNational 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 Research AreaMathematics ; Science & Technology - Other Topics
WOS SubjectMathematics, Interdisciplinary Applications ; Multidisciplinary Sciences
WOS IDWOS:000359318000017
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
Citation statistics
Cited Times:6[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/20530
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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