Permanence and extinction in logistic and Lotka-Volterra systems with diffusion

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	Permanence and extinction in logistic and Lotka-Volterra systems with diffusion
	Cui, JG ; Chen, LS
	2001-06-15
发表期刊	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
卷号	258 期号:2 页码:512-535
摘要	In this paper we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments. Differing from former studies, our discussion includes the important situation in conservation biology in which species live in a weak patchy environment, in the sense that species will become extinct in some of the isolated patches. For the single population model, we show that identical species can persist for some diffusion rates and can also vanish for another set of restrictions on the diffusion rates, although the single endangered species will vanish in some isolated patches without contributions from other patches. Furthermore, we consider the existence, uniqueness, and global stability of the positive periodic solution. For prey-predator systems we can make both the prey and the predator species permanent by choosing the diffusion rates appropriately, even if the prey species has a negative intrinsic growth rate in some patches. Moreover, we introduce an exotic competitive species y into the habitat occupied by the native species x. Competitive permanence and competitive exclusion bath are considered. The implications of these results are significant for the conservation of endangered species. (C) 2001 Academic Press.
关键词	logistic equation Lotka-Volterra system diffusion permanence extinction periodic solution stability
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000169264300010
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/16596
专题	中国科学院数学与系统科学研究院
通讯作者	Cui, JG
作者单位	1.Nanjing Normal Univ, Dept Math, Nanjing 210097, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Cui, JG,Chen, LS. Permanence and extinction in logistic and Lotka-Volterra systems with diffusion[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2001,258(2):512-535.
APA	Cui, JG,&Chen, LS.(2001).Permanence and extinction in logistic and Lotka-Volterra systems with diffusion.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,258(2),512-535.
MLA	Cui, JG,et al."Permanence and extinction in logistic and Lotka-Volterra systems with diffusion".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 258.2(2001):512-535.