Global Bifurcation of Positive Solutions in Some Systems of Elliptic Equations

Abstract

In this paper the structure of the nonnegative steady-state solutions of a system of reaction-diffusion equations arising in ecology is investigated. The equations model a situation in which a predator species and a prey species inhabit the same region and the interaction terms are of Holling–Tanner type sothat the predator has finite appetite. Prey and predator birth-rates are treated as bifurcation parameters and the theorems of global bifurcation theory are adapted so that they apply easily to the system. Thus ranges of parameters are found for which there exist nontrivial steady-state solutions.