The periodic solutions for general periodic impulsive population systems of functional differential equations and its applications

In this paper, the general periodic impulsive population systems of functional differential equations are investigated. By using the method of Poincare map and Horn's fixed point theorem, we prove that the ultimate boundedness of all solutions implies the existence of periodic solutions. As applications of this result, the existence of positive periodic solutions for the general periodic impulsive Kolmogorov-type population dynamical systems are discussed. We further prove that as long as the system is permanent, there must exist at least one positive periodic solution. In addition, the permanence and existence of positive periodic solutions are discussed for the periodic impulsive single-species logistic models and the periodic impulsive n-species Lotka-Volterra competitive models with delays. (C) 2011 Elsevier Ltd. All rights reserved.