S-SHAPED GLOBAL BIFURCATION CURVE OF POSITIVE SOLUTIONS TO A PREY-PREDATOR MODEL

YIHONG DU YUAN LOU

Abstract. The main purpose of this paper is to fully understand the structure of the set of all positive solutions to the prey-predator model with Holling-Tanner type interaction term. We confirm that the solutions curve can be S-Shaped as suggested by a number of previous local and numerical results.