We study the overdamped version of two coupled anharmonic oscillators under the influence of both low-and high-frequency forces respectively and a Gaussian noise term added to one of the two state variables of the system. The dynamics of the system is first studied in the presence of both forces separately without noise. In the presence of only one of the forces, no resonance behaviour is observed, however, hysteresis happens there. Then the influence of the high-frequency force in the presence of a low-frequency, i.e. biharmonic forcing, is studied. Vibrational resonance is found to occur when the amplitude of the high-frequency force is varied. The resonance curve resembles a stochastic resonance-like curve. It is maximum at the value of g at which the orbit lies in one well during one half of the drive cycle of the low-frequency force and in the other for the remaining half cycle. Vibrational resonance is characterized using the response amplitude and mean residence time. We show the occurrence of stochastic resonance behaviour in the overdamped system by replacing the high-frequency force by Gaussian noise. Similarities and differences between both types of resonance are presented.

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 c ) of f . This is found for all the forces except the modulus of sine and rectified sinusoidal forces. For fixed values of angular frequency ω of the periodic forces, f c is minimum for square wave and maximum for asymmetric sawtooth wave. f c is found to scale as Ae 0.75ω + B where A and B are constants.Stochastic resonance is observed in the presence of noise and periodic forces.The effect of different forces is compared. The stochastic resonance behaviour is quantized using power spectrum, signal-to-noise ratio, mean residence time and distribution of normalized residence times. The logarithmic plot of mean residence time τ MR against 1/(D − D c ) where D is the intensity of the noise and D 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 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 SN R peaks at a value of D for which sum of τ M R 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 ω, signal-to-noise ratio is found to be maximum for square wave while it is minimum for modulus of sine and 2 rectified sinusoidal waves. The values of D c at which cross-well behaviour is initiated and D max are found to depend on the shape of the periodic forces.

Vibrational and stochastic resonances (VR and SR) in two coupled overdamped anharmonic oscillators subjected to an amplitude modulated force are numerically studied. When both low- and high-frequency components are included the system show hysteresis and VR behaviour in the absence of a noise term. The resonance dynamics is characterized using response amplitude, phase portrait and mean residence time. We show the occurrence of SR by varying the noise intensity D in the presence of an amplitude modulated signal. High-frequency periodic force induced VR and noise-induced SR show certain similarities and differences.

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 τMR 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, τMR 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 τMR with D, the value of τMR 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.

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