Stochastic resonance with different periodic forces in overdamped two coupled anharmonic oscillators

摘要

We study the stochastic resonance phenomenon in the overdamped two coupledanharmonic oscillators with Gaussian noise and driven by different externalperiodic forces. We consider (i) sine, (ii) square, (iii) symmetric saw-tooth,(iv) asymmetric saw-tooth, (v) modulus of sine and (vi) rectified sinusoidalforces. The external periodic forces and Gaussian noise term are added to oneof the two state variables of the system. The effect of each force is studiedseparately. In the absence of noise term, when the amplitude $f$ of the appliedperiodic force is varied cross-well motion is realized above a critical value($f_{\mathrm{c}}$) of $f$. This is found for all the forces except the modulusof sine and rectified sinusoidal forces.Stochastic resonance is observed in thepresence of noise and periodic forces. The effect of different forces iscompared. The logarithmic plot of mean residence time $\tau_{\mathrm{MR}}$against $ 1/(D - D_{\mathrm{c}})$ where $D$ is the intensity of the noise and$D_{\mathrm{c}}$ is the value of $D$ at which cross-well motion is initiatedshows a sharp knee-like structure for all the forces. Signal-to-noise ratio isfound to be maximum at the noise intensity $D=D_{\mathrm{max}}$ at which meanresidence time is half of the period of the driving force for the forces suchas sine, square, symmetric saw-tooth and asymmetric saw-tooth waves. Withmodulus of sine wave and rectified sine wave, the $SNR$ peaks at a value of $D$for which sum of $\tau_{MR}$ in two wells of the potential of the system ishalf of the period of the driving force. For the chosen values of $f$ and$\omega$, signal-to-noise ratio is found to be maximum for square wave while itis minimum for modulus of sine and rectified sinusoidal waves.