  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.

Chaotic Dynamics