Regular Article - Statistical and Nonlinear Physics
Resonance behavior for a fractional underdamped bistable system with multiplicative and additive noise driven by one high-frequency and one low-frequency periodic signal
School of Automation Engineering, University of Electronic Science and Technology of China, 611731, Chengdu, China
2 School of Engineering, Karamay Campus, China University of Petroleum (Beijing), 834000, Karamay, China
3 School of Information Engineering, Southwest University of Science and Technology, 621010, Mianyang, China
Accepted: 19 December 2023
Published online: 31 January 2024
The stochastic resonance (SR) phenomenon for a fractional underdamped bistable system with multiplicative and additive noise driven by one high-frequency and one low-frequency periodic signal is investigated. The Fokker–Plank equation of the system for the low-frequency motion and the transition rate out of the system stable states are obtained. The signal-to-noise ratio (SNR) is derived based on two-state theory. It is shown that bona fide SR and bona fide vibration resonance (VR) phenomenon occur when the SNR varies with the frequency of the low-frequency signal and with that of the high-frequency signal, respectively. Single resonance peak appears when the SNR changes with the increase of the fractional exponent. Damping-induced SR takes place on the SNR curves versus the system damping coefficient. The SNR obtains one maximum value at certain levels of the multiplicative and additive noise.
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