IPM strategies to a discrete switching predator-prey model induced by a mate-finding Allee effect

Abstract

This paper proposes a discrete switching predator-prey model with a mate-finding Allee effect, where also switches are guided by Allee effect. One of the strategies analysed is to use a chemical in order to prevent the pest outbreak when the pest population is free of Allee effect. In this paper, we first study analytically the dynamic behaviors of the two subsystems and the equilibria and their stability of the switched system. Then we provide numerical bifurcation analyses for the switched discrete system. These show that the switched discrete system may have very complex dynamics by 2-parameter bifurcation diagrams which divide the space into regions and study equilibria, and 1-dimensional bifurcation diagrams which reveal that the system has periodic, chaotic solutions, period doubling bifurcations and so on. Furthermore, we try to refer the key parameters and initial densities of both populations associated with pest outbreaks and study their biological implications.