In order to describe the motion behavior of coupled particles with mass fluctuations in a viscous medium, this paper proposes a corresponding model, namely a fractional-order coupled system excited by trichotomous noise. Using the Shapiro-Loginov formula and the Laplace transform, we found the the statistical synchronization of the system, then the analytical expression of the system output amplitude gain is obtained. On this basis, this paper analyzes the influence 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. For examples, as the coupling coefficient increases, the generalized stochastic resonance phenomenon of the output amplitude gain of the system will first increase and then weaken until it converges. This phenomenon shows that the appropriate coupling strength can promote the generation of system resonance. With the order of the system Increases, the generalized stochastic resonance phenomenon of the system's output amplitude gain will gradually weaken. 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 the smallest. This phenomenon shows that the fractional order system can get a larger output amplitude gain than the traditional integer order system. The effect of the steady-state probability of noise on the output amplitude gain of the system will change with the changes of other related parameters. Under certain parameter conditions, trichotomous noise can not only make the output amplitude of the system be larger than the system which excited by dichotomous noise, and can also change the resonance type of the system. Finally, the correctness of the above results is verified by numerical simulation.
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