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The global dynamic behavior of the competition model of three species
Zhang, XA; Chen, LS
2000-05-01
Source PublicationJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN0022-247X
Volume245Issue:1Pages:124-141
AbstractIn this paper, we decompose the dynamic behavior of the competitive Lotka-Volterra (LV) model (x) over dot(i) = x(i)(1 - x(i) - alpha(i)x(i+1) - beta(i)x(i+2)), x(i)(0) > 0, alpha(i) > 0, beta(i) > 0, i = 1, 2, 3, with x(4) = x(1), x(5) - x(2), into the dynamic behavior of two two-dimensional manifolds, and completely analyse the global asymptotic behavior of the competitive LV model. We obtain the necessary and sufficient conditions for the equilibrium of the competitive LV model to be positive and globally asymptotically stable in Int R-+(3), the necessary and sufficient conditions for the model having a family of limit cycle solutions and a heteroclinic cycle, both of which are the omega-limit set of some other trajectories of the competitive LV model. (C) 2000 Academic Press.
Keywordextinction dominant local coordinate chart diffeomorphism
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000086866000009
PublisherACADEMIC PRESS INC
Citation statistics
Cited Times:10[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/15788
Collection中国科学院数学与系统科学研究院
AffiliationAcad Sinica, Inst Math, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Zhang, XA,Chen, LS. The global dynamic behavior of the competition model of three species[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2000,245(1):124-141.
APA Zhang, XA,&Chen, LS.(2000).The global dynamic behavior of the competition model of three species.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,245(1),124-141.
MLA Zhang, XA,et al."The global dynamic behavior of the competition model of three species".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 245.1(2000):124-141.
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