Abstract
The principal resonance of the stochastic Mathieu oscillator to randomparametric excitation is investigated. The method of multiple scales isused to determine the equations of modulation of amplitude and phase.The behavior, stability and bifurcation of steady state response arestudied by means of qualitative analyses. The effects of damping,detuning, bandwidth, and magnitudes of random excitation are analyzed.The explicit asymptotic formulas for the maximum Lyapunov exponent areobtained. The almost-sure stability or instability of the stochasticMathieu system depends on the sign of the maximum Lyapunov exponent.
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Rong, H., Meng, G., Wang, X. et al. Invariant Measures and Lyapunov Exponents for Stochastic Mathieu System. Nonlinear Dynamics 30, 313–321 (2002). https://doi.org/10.1023/A:1021208631414
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DOI: https://doi.org/10.1023/A:1021208631414