Asymptotic behavior of solutions of a class of delay differential systems

The asymptotic behavior of the bounded solutions of the delayed system {x′(t)=−F(x(t))+G(y(t−r)),y′(t)=−F(y(t))+G(x(t−r)), is investigated, where r>0r>0 is a given constant, FF, G∈C(R1)G∈C(R1), FF is strictly increasing on R1R1, and either G(x)≥F(x)G(x)≥F(x) for all x∈R1x∈R1 or G(x)≤F(x)G(x)≤F(x) for all x∈R1x∈R1. It is shown that every bounded solution of the system tends to a constant vector as t→∞t→∞. The result obtained extends the existing ones in the literature.