High multiplicity and global structure of coexistence states in a predator-prey model with saturation

Abstract

This paper establishes that, under the appropriate range of values of the parameters involved in the formulation of the model, a diffusive predator-prey system with saturation can have an arbitrarily large number of coexistence states for sufficiently large saturation rates. Moreover, it ascertains the global structure of the set of coexistence states in the limiting system as the saturation rate blows-up.