兰州大学机构库 >数学与统计学院
BIFURCATION AND SPATIOTEMPORAL PATTERNS IN A HOMOGENEOUS DIFFUSION-COMPETITION SYSTEM WITH DELAYS
Zhang, JF; Li, WT(李万同); Yan, XP; Li, WT (reprint author), Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China.
2012-11
Source PublicationInternational Journal of Biomathematics   Impact Factor & Quartile
ISSN1793-5245
Volume5Issue:6Pages:-
AbstractA competitive Lotka-Volterra reaction-diffusion system with two delays subject to Neumann boundary conditions is considered. It is well known that the positive constant steady state of the system is globally asymptotically stable if the interspecies competition is weaker than the intraspecies one and is unstable if the interspecies competition dominates over the intraspecies one. If the latter holds, then we show that Hopf bifurcation can occur as the parameters (delays) in the system cross some critical values. In particular, we prove that these Hopf bifurcations are all spatially homogeneous if the diffusive rates are suitably large, which has the same properties as Hopf bifurcation of the corresponding delayed system without diffusion. However, if the diffusive rates are suitably small, then the system generates the spatially nonhomogeneous Hopf bifurcation. Furthermore, we derive conditions for determining the direction of spatially nonhomogeneous Hopf bifurcations and the stability of bifurcating periodic solutions. These results indicate that the diffusion plays an important role for deriving the complex spatiotemporal dynamics.
KeywordLotka-volterra Competition System Time Delay Spatial Diffusion Hopf Bifurcation Periodic Solution
Subject AreaMathematical & Computational Biology
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
DOI10.1142/S1793524512500490
Publication PlaceSINGAPORE
Indexed BySCIE ; BIOSIS
Language英语
First Inst
Funding Project国家自然科学基金项目 ; 中央高校基本科研业务费专项资金
Project NumberFundamental Research Fund of Henan University [B2011088] ; NSFC [11031003, 10961017] ; FRFCU [lzujbky-2011-k27] ; "QingLan" Talent Program of Lanzhou Jiaotong University [QL-05-20A]
WOS IDWOS:000307850700002
Funding OrganizationNSFC ; LZU
SubtypeArticle
BIOSIS IDBIOSIS:PREV201200638223
Department[Zhang, Jia-Fang;
Li, Wan-Tong] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China;
[Zhang, Jia-Fang] Henan Univ, Sch Math & Informat Sci, Kaifeng 475001, Henan, Peoples R China;
[Yan, Xiang-Ping] Lanzhou Jiaotong Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China
Citation statistics
Cited Times:5[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/118623
Collection数学与统计学院
Corresponding AuthorLi, WT (reprint author), Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China.
Recommended Citation
GB/T 7714
Zhang, JF,Li, WT,Yan, XP,et al. BIFURCATION AND SPATIOTEMPORAL PATTERNS IN A HOMOGENEOUS DIFFUSION-COMPETITION SYSTEM WITH DELAYS[J]. International Journal of Biomathematics,2012,5(6):-.
APA Zhang, JF,Li, WT,Yan, XP,&Li, WT .(2012).BIFURCATION AND SPATIOTEMPORAL PATTERNS IN A HOMOGENEOUS DIFFUSION-COMPETITION SYSTEM WITH DELAYS.International Journal of Biomathematics,5(6),-.
MLA Zhang, JF,et al."BIFURCATION AND SPATIOTEMPORAL PATTERNS IN A HOMOGENEOUS DIFFUSION-COMPETITION SYSTEM WITH DELAYS".International Journal of Biomathematics 5.6(2012):-.
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