Bifurcation solution and stability on the unstirred chemostat system with B-D functional response

Abstract

This paper deals with the plasmid-bearing and plasmid-free model in the unstirred chemostat system with the Beddington-DeAngelis (denoted by B-D)functional response, which is a further development and continuation of [19] studied by Feng et al. The coexistence of local bifurcation solution is established by the local bifurcation theory, particularly, global structure of the local bifurcation solution is obtained by global bifurcation theory. Finally, the stability of non negative solutions is proved by the perturbation technique of eigenvalues.