Dynamic behavior for a system of neutral functional differential equations

Consider the system of neutral functional differential equations {(x1(t)−x2(t−r))′=−F(x1(t))+G(x2(t−r)),(x2(t)−x1(t−r))′=−F(x2(t))+G(x1(t−r)), where r>0r>0, FF, G∈C(R). It is shown that if FF is nondecreasing on R, 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 2r2r-periodic solutions. Our results are new and complement some corresponding ones already known.