Josef Hofbauer, Joseph W.-H. So:

Diagonal dominance and harmless off-diagonal delays.

Proc. Amer. Math. Soc. 128 (2000), 2675-2682.

Abstract. Systems of linear differential equations with constant coefficients, as well as Lotka-Volterra equations, with delays in the off-diagonal terms are considered. Such systems are shown to be asymptotically stable for any choice of delays if and only if the matrix has a negative weakly dominant diagonal.