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

A comparative study of asymmetric dichotomous noise and symmetric  trichotomous noise induced stochastic resonance in the globally coupled  fractional oscillators