The aim of this paper is to investigate the phenomena of stochastic resonance in an underdamped linear system with multiplicative trichotomous noise and an external periodic force. First, the exact expression of output amplitude gain of the system is obtained by using the Shapiro-Loginov procedure. The two kinds of stochastic resonance can be obtained for the output amplitude gain. One is called bona fide stochastic resonance, which induced by input signal frequency; the other is called general stochastic resonance which induced by noise flatness parameter or noise switching rate. And then, it is demonstrated that the output amplitude gain exhibits nonmonotonic dependence on the noise parameters (noise flatness parameter, noise switching rate etc). Finally, the influence of trichotomous noise and system parameters on output amplitude gain is analyzed by numerical method. The results show that the system damping rate restrained stochastic resonance, while noise switching rate enhanced noise flatness-induced stochastic resonance.
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