Abstract
Investigation on particle synchronization behavior and different kinds of stochastic resonance mechanism is reported in a fractional-order stochastic coupled system, which endures an external periodic excitation and polynomial asymmetric dichotomous noise damping disturbance. An extending of the method of stochastic averaging, the fractional Shapiro-Loginov formula and fractional Laplace transformation law are utilized, to determine the synchronization behavior between two coupled oscillators. The first moment of steady-state response and the output signal amplitude of the system are obtained in an analytical way, along with the stability condition. The crucial role of damping order and intrinsic frequency in stochastic resonance induced by noise intensity is explored, confirming the necessity of studying damping order falling in (1, 2). Due to the presence of nonlinear dichotomous colored noise, fresh phenomena of stochastic resonance and hypersensitive response induced by variation of external excitation frequency are found, where much more novel dynamical behaviors emerge than the non-disturbance case. It is confirmed that bimodal stochastic resonance only occurs for slow switching noise, with the damping order close to the parameter region of 0 or 2. For parameter-induced generalized stochastic resonance, explicit expressions of the critical damping strength corresponding to the optimal peak point of output amplitude are derived for the first time. By which different stochastic resonance patterns of the system under slow and fast switching noise perturbation are predicted successfully. In addition, the parametric effect and action mechanism of damping order on stochastic resonance are discussed in detail.