Stochastic resonance in overdamped two coupled anharmonic oscillators

Abstract

We consider the overdamped version of two coupled anharmonic oscillators with the external periodic force f sin ω t and Gaussian noise term η ( t ) added to one of the two state variables of the system. Linear stability analysis is carried out in the absence of external periodic force and noise. Then, the system with external periodic force only and noise term only are studied. In the noise free system, four period- T orbits are found to co-exist, one in each of the four wells for small values of forcing amplitude f for fixed values of other parameters. At a critical value of f, f c , cross-well periodic orbit appears. f c is found to increase with increase in the coupling strength δ . In the absence of forcing, the system is found to exhibit intermittent jumping motion between two wells above a particular value of noise strength D, D c . The noise-induced jumping behaviour is characterized by first-passage time and residence time distributions. Next, the influence of noise in the presence of the external periodic force is numerically studied. The system is found to exhibit stochastic resonance behaviour. The observed stochastic resonance dynamics is characterized using power spectrum, signal-to-noise ratio and residence time distribution. The plot of maximal Lyapunov exponent versus noise strength has shown a stochastic resonance profile. The occurrence of stochastic resonance is studied by varying the forcing frequency ω and the coupling strength δ . Finally, the influence of addition of external periodic force and noise term to different state variables is also presented.