Stability and Invariant Measures of Perturbed Dynamical Systems
For stability investigations of perturbed dynamical systems it is suitable to utilize the associated invariant measures in order to determine Lyapunov exponents of higher numerical accuracy. The densities of the invariant measures can be calculated by the stationary solutions of Fokker-Planck equations. The paper presents iterative schemes to solve these parabolic equations numerically and check the obtained results by means of Monte-Carlo simulations. Both methods are applied to oscillators perturbed by non-normal processes with bounded realizations.
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