In our former work (Eur. Phys. J. Plus 132, 432 (2017)), we investigated the stochastic resonance phenomenon in the overdamped bistable system with a fractional power nonlinearity. However, the analytical explanations are missing and the former work only considers the low-frequency signal excitation case. In the present work, we give the analytical result based on the two-state theory. Moreover, through the general scale transformation method, we make the stochastic resonance occur in the system with an arbitrary high-frequency excitation. Further, as a new result, we find that the fractional-order value can also induce stochastic resonance. The meaning of the study lies in its application in engineering fields. By finding the optimal fractional-order value, we can obtain a much higher signal-to-noise ratio in the signal processing issues. Numerical simulations and experimental vibration signal simulations verify the analytical results.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
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