Stochastic resonance of fractional-order coupled system excited by trichotomous noise

In order to describe the motion behavior of coupled particles with mass fluctuations in a viscous medium, we propose a corresponding model, namely a fractional-order coupled system excited by trichotomous noise. By using the Shapiro-Loginov formula and the Laplace transform, we find the statistical synchronization of the system, then obtain analytical expression of the system output amplitude gain. On this basis, this paper focuses on the key points, which are the coupled system, the fractional order system and the trichotomous noise, analyzes the influences of coupling coefficient, system order and noise steady-state probability on the generalized stochastic resonance phenomenon of system’s output amplitude gain, and gives some reasonable explanations. Specifically, first, as the coupling coefficient increases, the generalized stochastic resonance phenomenon of the output amplitude gain of the system first increases and then weakens until it converges. This phenomenon shows that the appropriate coupling strength can promote the generation of system resonance, thereby reflecting the importance of studying coupled systems. Second, with the order of the system increases, the generalized stochastic resonance phenomenon of the system’s output amplitude gain weakens gradually. When the system order value is 1, that is, when the system degenerates into an integer order system, the peak value of its output amplitude gain is smallest. This phenomenon shows that the fractional order system can obtain a larger output amplitude gain than the traditional integer order system. Third, the effect of the steady-state probability of noise on the output amplitude gain of the system changes with other related parameters. Under certain parameter conditions, trichotomous noise can not only make the output amplitude of the system larger than that of the system excited by dichotomous noise, but also change the resonance type of the system. Finally, the correctness of the above results is verified by numerical simulation.