On the Approximation of Delayed Systems by Taylor Series Expansion

Abstract

It is known that stability properties of delaydifferential equations are not preserved by Taylor series expansion of the delayed term. Still, this technique is often used to approximate delayed systems by ordinary differential equations in different engineering and biological applications. In this brief, it is demonstrated through some simple secondorder scalar systems that loworder Taylor series expansion of the delayed term approximates the asymptotic behavior of the original delayed system only for certain parameter regions, while for highorder expansions, the approximate system is unstable independently of the system parameters.