A Food Chain Model with a Protection Zone

Abstract

In this paper, we are concerned about a food chain model with a protection zone for the prey species. Dynamical behavior, nonexistence and existence of positive steady states are obtained and there exist several critical values determined by the parameters and the protection zone for the growth rate of the prey species. The results reveal that the protection zone is effective for the survival of the prey species and beneficial for the coexistence of multiple species. Moreover, different properties of positive steady states from those of the two-species models are shown. The introduction of the prey or the top predator can be either favorable or unfavorable for the coexistence of multiple species.

Keywords

Dynamical behavior / positive steady state / food chain model / protection zone