Bifurcation and Stability for the Unstirred Chemostat Model with Beddington-DeAngelis Functional Response

Abstract

In this paper, we consider a basic $N$-dimensional competition model in the unstirred chemostat with Beddington-DeAngelis functional response. The bifurcation solutions from a simple eigenvalue and a double eigenvalue are obtained respectively. In particular, for the double eigenvalue, we establish the existence and stability of coexistence solutions by the techniques of space decomposition and Lyapunov-Schmidt procedure. Moreover, we describe the global structure of these bifurcation solutions.