Janet Best

First Position

Dissertation

Advisor:

Abstract: In this thesis we use systems of ordinary differential equations to model competition between species. Coexistence is not possible in the competitive system; we ask when it can be embedded in a higher dimensional system with a predator species such that coexistence can occur in the full system. The form of predation is the same for all prey species up to parameter values.

Under suitable conditions on the parameters in the model, we prove that for three prey species and one predator species a sufficient condition for coexistence is that, as the density of a prey species approaches zero, the limit of the ratio of the per capita predation to the species density equals zero.

The proof constructs a function that blows up at the boundary and decreases along solutions near the boundary, thereby pushing solutions into the interior of the domain. It follows that after a finite amount of time, solutions are bounded away from the boundary and coexistence occurs.

Last modified: August 10, 2005