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Zbl 0799.92014
Lu, Zhengyi; Takeuchi, Yasuhiro
Global asymptotic behavior in single-species discrete diffusion systems. (English)
[J] J. Math. Biol. 32, No.1, 67-77 (1993). ISSN 0303-6812; ISSN 1432-1416/e

A single-species dynamical system is considered which is composed of several patches connected by discrete diffusion. Based on cooperative system theory and the property of a cooperative matrix, sufficient and necessary conditions are obtained for the system with linear diffusion to become extinct and for one with nonlinear diffusion to be globally stable. The authors obtain a critical patch number in the system with linear diffusion for the species to become extinct.
[A.I.Csetényi (Budapest)]

MSC 2000:: *92D25 Population dynamics
92D40 Ecology

Keywords: global stability; single-species dynamical system; discrete diffusion; cooperative system; cooperative matrix; sufficient and necessary conditions; linear diffusion; critical patch number

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