Effects of the Shape of Periodic Forces on Stochastic Resonance

We study the influence of the shapes of three different external periodic forces on the stochastic resonance phenomenon in multiple potential well systems with Gaussian noise. We consider as external periodic forces the sine wave, the modulus of sine wave and the rectified sine wave. The systems of our interest are two coupled overdamped anharmonic oscillators and the Duffing oscillator. For fixed values of the parameters, when the intensity D of the external noise is varied, the systems with these periodic forces separately are found to exhibit stochastic resonance. Certain similarities and differences are found in the characteristics of these statistical measures such as signal-to-noise ratio (SNR), response amplitude (Q), time series plot, mean residence time tau(MR) in the potential wells and the distribution P of the normalized residence time for these different forces. Especially, the time series plot at the maximum SNR shows an almost periodic switching between the potential wells for the sine force which is not observed for the other two forces. In the noise-induced intermittent dynamics, tau(MR) is the same in different wells for the sine force, whereas it is different in different wells for the other two forces for each value of the noise intensity D. Further, variation of tau(MR) with D, the value of tau(MR) at the resonance and the distribution P show different features for the different types of forces. We present a detailed comparative study and explanation for the similarities and differences observed in the stochastic resonance dynamics.