Asymptotic behavior of bounded solutions for a system of neutral functional differential equations ✩

Consider the system of neutral functional differential equations (x1(t) −cx2(t −r)) =−F(x1(t)) +G(x2(t −r)), (x2(t) −cx1(t −r)) =−F(x2(t)) +G(x1(t −r)), where r >0, c ∈ [0, 1), F, G ∈ C(R1) and F is strictly increasing on R1. It is shown that if F(x) G(x) for all x ∈ R1 or F(x) G(x) for all x ∈ R1, then every bounded solution of such a system tends to an equilibrium. Our results improve and extend some corresponding ones already known.  2005 Elsevier Inc. All rights reserved.