Dynamic Complexities of a Three-Species Beddington-DeAngelis System with Impulsive Control Strategy

By introducing the impulsive control strategy, the dynamical properties of the three-species food chain systems with Beddington-DeAngelis functional response are investigated. Using the Floquet theory of impulsive differential equations and small amplitude perturbation techniques, we prove that there exists an asymptotically locally stable prey-free periodic solution under some conditions, and permanence conditions are established via the comparison theorem. Furthermore, from numerical examples, we figure out that the system has complex dynamic behaviors.