Stochastic Stability Criteria for Second-Order Oscillator Parametrically Excited by Colored Noise

A second order oscillator is considered having a random perturbation in its stiffness. This is given by a colored Gaussian or non-Gaussian process. In this way, the oscillator may stochastically stable or unstable according to the intensity of the excitation. The almost sure (sample) stochastic stability and the stability in the first three response statistical moments are compared for different excitation proc-esses: process with exponential autocorrelation, second order Gaussian process, bounded noise proc-ess. Notable differences in the stability boundaries are found either according to the stability criteria or to the type of excitation. These comparisons are lacking in literature.