Positive steady states for a prey–predator model with population flux by attractive transition

Abstract

This paper studies the stationary solutions of a prey–predator model with population flux by attractive transition. We first obtain a bifurcation branch (connected set) of positive solutions which connects two semitrivial solutions. Next we derive the asymptotic behavior of positive solutions as the coefficient α of the population flux tends to infinity. A main result implies that positive solutions can be classified into two types as α→∞. In one type of them, as α→∞, positive solutions of the prey–predator model approach positive solutions of a competition model with equal diffusion coefficients.