The stable coexistence of competing species on a renewable resource

AbstractWe consider a system of three autonomous ordinary differential equations modeling two competing species for a prey resource. We obtain a simple criterion in terms of the specific growth of the prey for there to be an asymptotically stable equilibrium. In a special case, we show that a Hopf bifurcation about this equilibrium could occur. In another special case we show that the interior equilibrium could be globally asymptotically stable. The results are illustrated by a numerical example. Finally it is shown that in the general case, not all competition models posess the properties described in this paper