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Zeitschrift für Analysis und ihre Anwendungen


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Volume 23, Issue 1, 2004, pp. 17–38
DOI: 10.4171/ZAA/1186

Published online: 2004-03-31

Extinction and Asymptotic Behavior of Solutions to a System Arising in Biology

M. Kouche[1] and Nasser-edine Tatar[2]

(1) University Badji Mokhtar, Annaba, Algeria
(2) King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

A generalization to n species of a system by L. Bass, A. J. Bracken, K. Holmaker and B. Jefferies [J. Austral. Math. Soc. (Ser. B) 29 (1987) 156--194], which describes the self-organization of liver zones in a liver capillary in the case of two species, is proposed. We establish some hypotheses on the coefficient parameters of the system under which a part of the species is driven to extinction while the remaining ones are attracted by the non-trivial stationary solution.

Keywords: Coexistence, extinction, global asymptotic stability, integro-differential system, logistic equation, Lyapunov function, persistence

Kouche M., Tatar Nasser-edine: Extinction and Asymptotic Behavior of Solutions to a System Arising in Biology. Z. Anal. Anwend. 23 (2004), 17-38. doi: 10.4171/ZAA/1186