Stability of the Damped Mathieu Equation With Time Delay

Abstract

In the space of the system parameters, the stability charts are determined for the delayed and damped Mathieu equation defined as ẍ(t)+κẋ(t)+(δ+ε cos t)x(t)=bx(t−2π). This stability chart makes the connection between the Strutt-Ince chart of the damped Mathieu equation and the Hsu-Bhatt-Vyshnegradskii chart of the autonomous second order delay-differential equation. The combined charts describe the intriguing stability properties of an important class of delayed oscillatory systems subjected to parametric excitation.