an:02149058
Zbl 1056.34073
Insperger, T.; St??p??n, G.
Stability chart for the delayed Mathieu equation
EN
Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2024, 1989-1998 (2002).
00086585
2002
j
34K20 34C15 70K40
parametric excitation; time delay; stability
Summary: In the space of system parameters, the closed-form stability chart is determined for the delayed Mathieu equation defined as \(\ddot x(t)+(\delta+ k\cos t)x(t)= bx(t-2\pi)\). 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.