Some Extension of Hara-Sugie Stability Condition by Using Critical Delay

Abstract

The transcendency of the characteristic equation of a linear delay differential equation (DDE) with a delay parameter is a main feature that creates a difference from ordinary differential equations. Here we discuss a method to find the stability condition of the characteristic equation of a planar system of linear DDEs by using the critical delay, which is the threshold delay value dividing the stability and instability regions of the characteristic equation. This method gives a clear understanding of the nature of stability of characteristic equations of some class of linear DDEs, and the obtained results are considered to be an extension of the previous result obtained by Hara and Sugie [Funkcial. Ekvac., 39 (1996), 69-86].