An interference effect of independent delays

For a second-order linear retarded delay-differential equation with two independent delays, two methods are used to demonstrate an interference effect that can reduce the likelihood of instability. Both methods rely on the basic result that stability changes only take place at pure imaginary values of the complex eigenvalue. One method uses the eliminant, which is zero if and only if both real and imaginary parts of the characteristic equation are satisfied. The other is an extension of a method used in problems with one delay, in which a certain curve is plotted to find whether it intersects the unit circle. When this interference effect is present, equal delays are particularly unlikely to destabilise.