Dynamics analysis of a predator–prey model with nonmonotonic functional response and impulsive control

Abstract

This paper presents the qualitative analysis of a predator–prey model with nonmonotonic functional response and impulsive effects. Different from previous work, by considering two factors of nonmonotonic functional response and impulsive effects, this paper studies the existence and stability of the periodic semi-trivial solution y=0 first. Then, by constructing an appropriate Poincare map and introducing geometric theory, it is shown that the predator–prey model can exhibit a variety of dynamic phenomena, including orbitally asymptotically stable order-1 periodic solution (O1PS), order-2 periodic solution (O2PS) and globally stable equilibrium point under certain conditions. When there exists an O2PS, its appearance and disappearance as well as the appearance of bifurcation phenomenon are discussed in detail with different selections of the initial value of predator. Finally, numerical simulations illustrate the correctness of the results of the theoretical analysis. The theoretical results presented in this paper can be seen as an advancement to the previous related works.