On the Dynamics of Impulsive Predator-Prey Systems With Beddington-DeAngelis Functional Response

Abstract

We study a two-dimensional predator-prey system with Beddington-DeAngelis-type functional response with pulses in a periodic environment. In the analyzed special case, we establish necessary and sufficient conditions for the considered system to have at least one w-periodic solution. This result is mainly based on the continuation theorem from the coincidence-degree theory. Moreover, in order to find the globally attractive w-periodic solution of the system, by using the analytic structure of the given system, we deduce an inequality playing the role of both necessary and sufficient condition.