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Stability chart for the delayed Mathieu equation. (English) Zbl 1056.34073
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.

##### MSC:
 34K20 Stability theory of functional-differential equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 70K40 Forced motions for nonlinear problems in mechanics
##### Keywords:
parametric excitation; time delay; stability
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