Diagonal dominance and harmless off-diagonal delays
Josef Hofbauer, Joseph W.-H. So · Proceedings of the American Mathematical Society · 2000
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.