Complete mathematical analysis of predator–prey models with linear prey growth and Beddington–DeAngelis functional response

Abstract

The dynamics of a predator–prey model with a Beddington–DeAngelis functional response and linear intrinsic growth rate of the prey population is fully analyzed. Conditions on local and global stability of the interior equilibrium are established. The equilibria type are determined. All possible global asymptotic behaviors of the system are considered, including the determination of the extinction conditions and existence of periodic orbits. It is shown that mutual interference between predators can alone stabilize predator–prey interactions even when only a linear intrinsic growth rate of the prey population is considered in the mathematical model. Additional biological implications and a set of numerical simulations supporting the analysis are also presented.