A food chain model for two resources in un-stirred chemostat

This paper deals with a multiple food chain model in un-stirred chemostat, where the prey feeds on two growth-limiting, nonreproducing resources. The conditions for existence of positive steady states are established. The global bifurcation of positive solutions is considered also. Furthermore, we obtain the conditions under which the predator possesses uniformly strong persistence or goes to extinction. The techniques used in this paper include the degree theory, the global bifurcation theory, the semigroup theory, and the maximum principle.