Bifurcation Analysis for a Food Chain Model with Nonmonotonic Nutrition Conversion Rate of Predator to Top Predator

Abstract

In this paper, a prey–predator-top predator food chain model with nonmonotonic functional response in the predators is studied. With an emphasis on the nutrition conversion rate of predator to top predator, one can get two important thresholds: the top predator extinction threshold and the coexistence threshold. The top predator will die out if the nutrition conversion rate of predator to top predator is less than the top predator extinction threshold; the prey, predator and top predator will coexist if the rate is larger than the coexistence threshold. While between the two thresholds is a bistable interval. When the nutrition conversion rate of predator to top predator is in the bistable interval, the system will see the emergence of bistability. The bifurcation analysis of the system depending on parameters indicates that it exhibits saddle-node bifurcation and Hopf bifurcation phenomena.