The periodic competing Lotka-Volterra model with impulsive effect.

Abstract

In this paper, the dynamic behaviour of a classical periodic Lotka-Volterra competing system with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equations, some conditions are obtained for the linear stability of the trivial and semi-trivial periodic solutions. It is proved that the system can be permanent if all the trivial and semi-trivial periodic solutions are linearly unstable. We use standard bifurcation theory to show the existence of nontrivial periodic solutions which arise near the semi-trivial periodic solution. As an application, a fish harvest problem is considered. We explain how two competing species, one of which in a periodic environment without impulsive effect would be doomed to extinction, can coexist with suitably periodic impulsive harvesting.