Dynamic behavior for a system of neutral functional differential equations

Consider the system of neutral functional differential equations (x(1)(t) - x(2)(t - r))' = -F(x(1)(t)) + G(x(2)(t - r)), (x(2)(t) - x(1)(t - r))' = -F(x(2)(t)) + G(x(1)(t - r)), where r > 0, F, G is an element of C(R). It is shown that if F is nondecreasing on R. and some additional assumptions hold, then the omega limit set of every bounded solution of such a system with some initial conditions is composed of 2r-periodic solutions. Our results are new and complement some corresponding ones already known. (C) 2009 Elsevier Ltd. All rights reserved.