JournalszaaVol. 23 , No. 1DOI 10.4171/zaa/1186

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

  • M. Kouche

    University Badji Mokhtar, Annaba, Algeria
  • Nasser-edine Tatar

    King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Extinction and Asymptotic Behavior of Solutions to a System Arising in Biology cover

Abstract

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.