New generalization of the two-dimensional Bernfeld–Haddock conjecture and its proof

In this paper, we investigate a class of systems of delay differential equations. These systems have important practical applications and also are a two-dimensional generalization of the Bernfeld–Haddock conjecture. It is shown that each bounded solution of the systems tends to a constant vector under a desirable condition. Our results improve some corresponding ones already known and, in particular, give a proof of the Bernfeld–Haddock conjecture.