We present a small ε perturbation analysis of the quasiperiodic Mathieu equation:
x¨+(δ+εcost+εcosωt)x=0
in the neighborhood of the point δ = 0.25 and ω = 0.5. We use multiple scales including terms of O2) with three time scales. We obtain an asymptotic expansion for an associated instability region. Comparison with numerical integration shows good agreement for ε = 0.1. Then we use the algebraic form of the perturbation solution to approximate scaling factors which are conjectured to determine the size of instability regions as we go from one resonance to another in the δ-ω parameter plane.
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