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Abstract: Sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the delay differential system with feedback controlThe method involves the application of Krasnoselskii''s fixed point theorem and estimates of uniform upper and lower bounds of solutions. When these results are applied to some special delay population models with multiple delays, some new results are obtained and some known results are generalized. [Copyright &y& Elsevier]

In this paper we shall consider the following nonlinear impulsive delay differential equation where m and n are positive integers, V(t) and λ(t) are positive periodic continuous functions with period ω>0. In the nondelay case (m=0), we show that the above equation has a unique positive periodic solution x*(t) which is globally asymptotically stable. In the delay case, we present sufficient conditions for the global attractivity of x*(t). Our results imply that under the appropriate periodic impulsive perturbations, the impulsive delay equation shown above preserves the original periodic property of the nonimpulsive delay equation. In particular, our work extends and improves some known results. [Copyright &y& Elsevier]