Abstract
Stability investigations of perturbed dynamical systems are considerably refined by utilizing the invariant measures of the systems, which can be calculated by the stationary solutions of the associated Fokker-Planck equations. The paper presents iterative schemes in order to obtain these solutions as limit cycles and check them by means of Monte-Carlo simulations. Both methods are applied to parametrically excited oscillators including the limiting cases of deterministic harmonic excitations and stochastic white noise perturbations.
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