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

We study the stochastic resonance phenomenon in the overdamped two coupled anharmonic oscillators with Gaussian noise and driven by different external periodic forces. We consider (i) sine, (ii) square, (iii) symmetric saw-tooth, (iv) asymmetric saw-tooth, (v) modulus of sine and (vi) rectified sinusoidal forces. The external periodic forces and Gaussian noise term are added to one of the two state variables of the system. The effect of each force is studied separately. In the absence of noise term, when the amplitude $f$ of the applied periodic 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 modulus of sine and rectified sinusoidal forces.Stochastic resonance is observed in the presence of noise and periodic forces. The effect of different forces is compared. 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 initiated shows a sharp knee-like structure for all the forces. Signal-to-noise ratio is found to be maximum at the noise intensity $D=D_{\mathrm{max}}$ at which mean residence time is half of the period of the driving force for the forces such as sine, square, symmetric saw-tooth and asymmetric saw-tooth waves. With modulus 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 is half 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 it is minimum for modulus of sine and rectified sinusoidal waves.Comment: 13 figures,27 page

Experimental evidence for vibrational resonance and enhanced signal transmission in Chua's circuit

We consider a single Chua's circuit and a system of a unidirectionally coupled n-Chua's circuits driven by a biharmonic signal with two widely different frequencies \omega and \Omega, where \Omega >> \omega. We show experimental evidence for vibrational resonance in the single Chua's circuit and undamped signal propagation of a low-frequency signal in the system of n-coupled Chua's circuits where only the first circuit is driven by the biharmonic signal. In the single circuit, we illustrate the mechanism of vibrational resonance and the influence of the biharmonic signal parameters on the resonance. In the n(= 75)-coupled Chua's circuits enhanced propagation of low-frequency signal is found to occur for a wide range of values of the amplitude of the high-frequency input signal and coupling parameter. The response amplitude of the ith circuit increases with i and attains a saturation. Moreover, the unidirectional coupling is found to act as a low-pass filter.Comment: 15 pages, 12 figures, Accepted for Publication in International Journal of Bifurcation and Chao