Periodic solution and heteroclinic bifurcation in a predator–prey system with Allee effect and impulsive harvesting

Abstract

In this article, we investigate a prey– predator model with Allee effect and state-dependent impulsive harvesting. We obtain the sufficient conditions for the existence and uniqueness of order-1 periodic solution of system (1.2) by means of the geometry theory of semicontinuous dynamic system and the method of successor function. We also obtain that system (1.2) exhibits the phenomenon of heteroclinic bifurcation about parameter \(\alpha \). The methods used in this article are novel and prove the existence of order-1 periodic solution and heteroclinic bifurcation.