Global attractivity of positive periodic solution to periodic Lotka-Volterra competition systems with pure delay

We consider a periodic Lotka-Volterra competition system without instantaneous negative feedbacks (i.e., pure-delay systems) x(i)(t) = x(i)(t)[r(i)(t) - Sigma(n)(j=1) a(ij)(t - tau(ij)(t))], i = 1,2,...,n. some 3/2-type criteria for global attractivity of a positive periodic solution of the system, which generalize the well-known Wright's 3/2 criteria for the autonomous delay logistic equation, and thereby, address the open problem proposed by both Kuang [Y. Kuang, Global stability in delayed nonautonomous Lotka-Volterra type systems without saturated equilibria, Differential Integral Equations 9 (1996) 557-567] and Teng [Z. Teng, Nonautonomous Lotka-Volterra systems with delays, J. Differential Equations 179 (2002) 538-5611. (c) 2006 Elsevier Inc. All rights reserved.