A discussion of stability analysis for systems of differential equations with multiple and distributed delays

Abstract

In this article, we consider a class of systems of multiple delay differential equations (MDDEs). We first define a characteristic matrix equation that can be used to analyze the stability of the equilibrium of a system of MDDEs. Then we construct a matrix based on the coefficients of the characteristic matrix equation and use the spectrum of this matrix to derive necessary and sufficient conditions for the system to be stable. Next we discuss a comparison of the stability equivalency between a system of delay differential equations (DDEs) to the system of MDDEs and relate our results to distributed delay systems (DDSs). Numerical examples are given to justify our theory.