Cooperative Systems Theory and Global Stability of Diffusion Models

Y. Takeuchi
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Y. Takeuchi: Shizuoka University, Department of Applied Mathematics, Faculty of Engineering

A chapter in Evolution and Control in Biological Systems, 1989, pp 49-57 from Springer

Abstract: Abstract Many authors consider the effect of spatial factors, such as diffusion or migration among patches, in population dynamics. We suppose that the system is composed of several patches connected by diffusion and occupied by a single species. Furthermore, the species is supposed to be able to survive in all the patches at a positive globally stable equilibrium point if the patches are isolated, or if the diffusion among patches is neglected and the species is confined to each patch. The problem considered in this paper is whether the equilibrium point, the value of which can be changed according to the strength of diffusion, continues to be positive and globally stable, if we increase the rates of diffusion.

Keywords: 92A17; 34D20; global stability; cooperative systems; diffusion (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-94-009-2358-4_6

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