Dynamic behavior for a system of neutral functional differential equations

AbstractConsider 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>0, F, G∈C(R). It is shown that if F is nondecreasing on R, and some additional assumptions hold, then the ω 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