Stability chart for the delayed Mathieu equation

Abstract

In the space of system parameters, the closed–form stability chart is determined for the delayed Mathieu equation defined as ä(t)+(δ+εcost)x(t) = bx(t−2π). This stability chart makes the connection between the Strutt–Ince chart of the Mathieu equation and the Hsu–Bhatt–Vyshnegradskii chart of the second–order delay–differential equation. The combined chart describes the intriguing stability properties of a class of delayed oscillatory systems subjected to parametric excitation.