Large saturation effects provoke multiplicity in spatially heterogeneous predator-prey models

Abstract

This communication analyzes the diffusive spatially heterogeneous predator-prey model introduced by the authors in [16], which takes into account the saturation effects of the predator in the abundance of preys through a saturation coefficient $\gamma m(x)\neq0$ with $\|m\|_{\infty}=1$. The main result establishes the existence of, at least, two coexistence states for sufficiently large $\gamma>0$ in a region of the parameters where the Lotka–Volterra counterpart cannot admit any coexistence state, regardless the size and shapes of the logistic and interactions coefficients of the model.