The role of damping on Stochastic Resonance in a periodic potential

The role of damping on the phenomenon of Stochastic Resonance (SR) in a driven underdamped periodic potential system is studied. Using input energy per period of external drive as a quantifier, SR is observed in the model multistable system in the high frequency regime, due to the noise assisted transitions of the particle between two distinct dynamical states of trajectories, characterized by their definite amplitude, energy and phase. SR is observed in this system only when the damping is lesser than a particular maximum limit. The stability of the two states and hence the nature of SR depends upon the damping parameter γ and the amplitude of drive. The input energy distributions at different temperatures across the SR peak, bear characteristic features associated with SR. The average input energy 〈Ei¯〉 per period of external drive peaks as a function γ. The phase difference ϕ̄ between the particle's average response amplitude and the external drive plotted as a function of γ shows an inflection point corresponding to the peak in 〈Ei¯〉. Thus inflection in ϕ̄ is not exclusive only to SR peaks.