Stability sets for linear differential-difference equations with two delays (Q2761984)

The author studies the stability set, that is the set of \((a, b)\) for which the zero solution to the scalar linear differential-difference equation with two delays NEWLINE\[NEWLINE \dot{x}(t)=ax(t-\tau_1)+bx(t-\tau_2) NEWLINE\]NEWLINE is asymptotically stable. Especially, by using root-analysis for the characteristic equation, he obtains that the stability set for the case of \(\tau_2=2\tau_1\) is a region enclosed by a line and a curve, but the one for the case of \(\tau_2=3\tau_1\) is the union of two regions.