Deterministic and Stochastic Prey–Predator Model for Three Predators and a Single Prey

Abstract

In this paper, a deterministic prey–predator model is proposed and analyzed. The interaction between three predators and a single prey was investigated. The impact of harvesting on the three predators was studied, and we concluded that the dynamics of the population can be controlled by harvesting. Some sufficient conditions were obtained to ensure the local and global stability of equilibrium points. The transcritical bifurcation was investigated using Sotomayor’s theorem. We performed a stochastic extension of the deterministic model to study the fluctuation environmental factors. The existence of a unique global positive solution for the stochastic model was investigated. The exponential–mean–squared stability of the resulting stochastic differential equation model was examined, and it was found to be dependent on the harvesting effort. Theoretical results are illustrated using numerical simulations.