The global dynamic behavior of the competition model of three species

CSpace

	The global dynamic behavior of the competition model of three species
	Zhang, XA; Chen, LS
	2000-05-01
发表期刊	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
卷号	245 期号:1 页码:124-141
摘要	In 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.
关键词	extinction dominant local coordinate chart diffeomorphism
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000086866000009
出版者	ACADEMIC PRESS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/15788
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, XA
作者单位	Acad Sinica, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 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.