In this work, we investigate regions of stability in the vicinity of 2:2:1 resonance in the quasiperiodic Mathieu equation:
using two successive perturbation methods. The parameters ε and μ are assumed to be small. The parameter ε serves for deriving the corresponding slow flow differential system and μ serves to implement a second perturbation analysis on the slow flow system near its proper resonance. This strategy allows us to obtain analytical expressions for the transition curves in the resonant quasiperiodic Mathieu equation. We compare the analytical results with those of direct numerical integration. This work has application to parametrically excited systems in which there are two periodic drivers, each with frequency close to twice the frequency of the unforced system.
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