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