AMCA: Competitive systems with three species and periodic coefficients by Rafael Ortega

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Equadiff 2003 - International Conference on Differential Equations
July 22-26, 2003
LUC Diepenbeek
Hasselt, Belgium

Organizers
Freddy Dumortier (Chair, LUC Diepenbeek), Henk Broer (Univ. Groningen), Jean-Pierre Gossez (Univ. Libre Bruxelles), Jean Mawhin (Univ. Cath. Louvain-la-Neuve), Andre Vanderbauwhede (Univ. Gent), Sjoerd Verduyn Lunel (Univ. Leiden)

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Competitive systems with three species and periodic coefficients
by
Rafael Ortega
Universidad de Granada

Consider the competitive system

×

u

i
=u_i (a_i(t)- 3
å
j=1
b_ij (t)u_j ) , u_i >= 0, i=1, 2, 3,

where the coefficients a_i and b_ij are periodic functions of the same period T and all coefficients b_ij are positive. More general models of the type

×

u

i
=u_i f_i(t, u₁ , u₂ , u₃ ), u_i >= 0, i=1, 2, 3

are also considered. A T-periodic solution u(t) is a coexistence state if u_i (t) > 0 for each i. We discuss the dynamics of these systems in the absence of coexistence states. For analytic systems (and hence for the Lotka-Volterra model) there is always extinction. For non-analytic systems there are other possibilities. These results are linked to the study of the dynamics of a homeomorphism of the disk having no fixed points in the interior.

Date received: May 16, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # calh-39.