Qualitative behavior of a variable-yield simple food chain with an inhibiting nutrient

A simple food chain which consists of nutrient, prey and predator in which nutrient is growth limiting at low concentrations but growth inhibiting at high concentrations is investigated in this study. It is assumed that the nutrient concentration is separated into internal and external nutrient concentration and only the internal nutrient level is capable of catalyzing cell growth. It is shown that the dynamics of the system depend on thresholds R(0) and R(1). With inhibition, there exist initial conditions for which the predator becomes extinct but not the prey when R(0)<1. If R(0),R(1)1, the system is uniformly persistent even in the inhibited environment.