Analysis of a predator-prey system with Beddington-type functional response and stage-structure of prey

Abstract

Abstract:Taking into account stage-structure for prey and periodic pulse at different fixed moments, a delayed prey-predator system with Beddington-type functional response was investigated. Applying the small amplitude perturbation method and Floquet's theory, we obtained the sufficient conditions for the local stability, globally asymptotical stability and global attractivity of the prey-extinction periodic solution. Further, by using theories of impulsive differential equation and delay differential equation, we obtained the conditions of the permanence of this system. Finally, examples and numerical simulations are given to show the complex dynamic behaviours of the system. Especially, we find that the impulsive and the time delay play an important role in the permanence of the system.