  The collective behaviour, in respect of stochastic resonance, has been
studied in globally coupled oscillators (with fractional-order intrinsic and
external damping), driven by a sinusoidal force which is either noise-free or
noise-modulated, and subjected to multiplicative quadratic asymmetric
dichotomous or symmetric trichotomous noise perturbing the potential parameter,
the coupling factor and the local drift force. The influence of coupling
between the heat bath and the applied force has been included through a simple
model. The effect of variation in mass, friction and potential parameters on
the output amplitude gains as function of noise-intensity, has been
meticulously investigated for both types of noise and the exponents governing
the dependence of collective SR peak amplitude on the three oscillator
parameters have been determined and analysed. The special case arising from the
zero value of the potential parameter, which implies rectilinear motion of the
system particles in the absence of fluctuations, has been dealt with under the
influence of the second-order asymmetric dichotomous noise and stochastic
resonance has been found to occur at justifiably quite low frequencies of the
external force. This brings out the importance of nonlinear term in this
coloured noise, for which this phenomenon is unique. The accuracy of the
analytical results has been substantiated through numerical simulations.
