Dynamic behavior for a system of neutral functional differential equations

Consider the system of neutral functional differential equations .x1.t/ 􀀀 x2.t 􀀀 r//0 D 􀀀F .x1.t// C G.x2.t 􀀀 r//; .x2.t/ 􀀀 x1.t 􀀀 r//0 D 􀀀F .x2.t// C G.x1.t 􀀀 r//; where r > 0, F , G 2 C.R/. It is shown that if F is nondecreasing on R, and some additional assumptions hold, then the ! 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.