Construction of Positive Invariant Sets in a Prey-predator Model with the Holling Type II Nonlinearity

Abstract

Abstract. The prey-predator model with the Holling type II nonlinearity is a twocomponent reaction diffusion equations. We construct some time-independent positive invariant sets for this equations when the diffusion coefficients are common to the prey and predator. Namely, there is a region in the phase space where the time evolution stays at any instant as far as the initial condition is within there. These positive invariant sets are constructed from the fact that they coincide with those of the ordinary differential equations which are obtained by omitting the diffusion terms from the original reaction diffusion system.