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)equation(*)x˙i(t)=xi(t)[ri(t)−∑j=1naij(t)xj(t−τij(t))],i=1,2,…,n. We establish 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) 538–561].