UMR 5466, Mathematiques Appliquees de Bordeaux
case 26, Universite Victor Segalen Bordeaux 2
33076 Bordeaux Cedex France.
telephone/fax : +33 (0) 5 57 57 15 37
Structured population dynamics problems with spatial migration: application to heterogeneous insular populations
Island ecosystems offer very specific features, especially spatially heterogeneous remote islands found in the subantartic area.
Native species, e.g., birds, often possess limited antipredation or competition behaviors.
Accidentally or deliberately introduced species such as cats, rats or rabits thus become threats for endemic populations and their persistence.
It may become necessary to control their growth or eradicate these alien species.
This talk is made of two parts.
First we analyze an epidemic problem modelling the propagation of a virus designed to eradicate a feral population; this is motivated by an experiment conducted on Marion Island in 1977/1991 .
Next we develop a predator-prey population model adapted to such typical insular conditions, with a very rich dynamical behavior possibly featuring finite time extinction of both native and alien species.
Using numerical experiment we show some interesting dynamics when spatial heterogeneities are introduced in the model.