Stochastic resonance in an overdamped system with a fractional power nonlinearity: Analytical and re-scaled analysis
School of Mechatronic Engineering, China University of Mining and Technology, 221116, Xuzhou, China
2 Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, China University of Mining and Technology, 221116, Xuzhou, China
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Accepted: 17 December 2018
Published online: 21 March 2019
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.
© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2019