Stochastic resonance in two coupled fractional oscillators with potential and coupling parameters subjected to quadratic asymmetric dichotomous noise

Abstract

Exact analytical expressions for the average output amplitude gains in the very long-time limit for two coupled oscillators governed by fractional-order intrinsic and external damping, under the influence of a multiplicative quadratic asymmetric dichotomous noise affecting the two potential parameters and the coupling factors, and subjected to a noise-free or noise-modulated external periodic force with same frequency, have been derived. The trustworthiness of the analytical expressions has been checked by comparing the numerical results obtained using these for some typical cases with corresponding findings based on numerical simulations. The numerical simulations have also been used to investigate the time-evolution of a representative system in the transient state by studying the probability density and displacements of the two oscillators at different times and for different values of noise intensity. Analytical expressions have been used to obtain plots for gains versus noise intensity to study the effect of (i) variation in mass parameter of one oscillator keeping that of other the same, and (ii) change in the relative values of the two coupling coefficients. Furthermore, the special case where both the potential parameters are taken to be zero, which corresponds to rectilinear motion of the two particles in the absence of fluctuations, has been examined under the influence of the second-order noise and stochastic resonance has been found to occur at lower frequencies of the applied force. This highlights the importance of nonlinear term in the noise, which makes the rectilinear motion to be oscillatory. Also, the key role played by the coupling in this has been brought out.