We carry out a detailed numerical investigation of stochastic resonance inunderdamped systems in the non-perturbative regime. We point out that animportant distinction between stochastic resonance in overdamped andunderdamped systems lies in the lack of dependence of the amplitude of thenoise-averaged trajectory on the noise strength, in the latter case. We providequalitative explanations for the observed behavior and show that signaturessuch as the initial decay and long-time oscillatory behaviour of the temporalcorrelation function and peaks in the noise and phase averaged power spectraldensity, clearly indicate the manifestation of resonant behaviour in noisy,underdamped bistable systems in the weak to moderate noise regime.
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