Abstract
In this paper, a classical periodic Lotka–Volterra predator-prey system with impulsive effect is investigated. We analyze the dynamics of positive solutions of such models. Among other results we show that if some trivial or semi-trivial positive solution is linearly stable, then it is globally asymptotically stable with respect to the positive solutions. By using the method of coincidence degree, a set of sufficient conditions are derived for the existence of at least one strictly positive (componentwise) periodic solution. We use bifurcation theorem to show the existence of coexistence states which arise near the sem-trivial periodic solution. As an application, we also examine some special cases of the system which can be used in the biological pest control.
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