ωω limit sets of solutions for a class of neutral functional differential equations

Consider the system of neutral functional differential equations {(x1(t)−x2(t−r2))′=−F1(x1(t))+G1(x2(t−r2)),(x2(t)−x1(t−r1))′=−F2(x2(t))+G2(x1(t−r1)), where ri>0ri>0, and FiFi, Gi∈C(R1),i=1,2Gi∈C(R1),i=1,2. It is shown that if Fi(i=1,2) is nondecreasing on R1R1, and some additional assumptions hold, then the ωω limit set of every bounded solution of such a system with some initial conditions is composed of (r1+r2)(r1+r2)-periodic solutions. Our results are new and complement some corresponding ones already known.