Resonance behavior for a fractional underdamped bistable system with multiplicative and additive noise driven by one high-frequency and one low-frequency periodic signal

Zhiqi Huang () and Feng Guo
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Zhiqi Huang: University of Electronic Science and Technology of China
Feng Guo: Southwest University of Science and Technology

The European Physical Journal B: Condensed Matter and Complex Systems, 2024, vol. 97, issue 1, 1-12

Abstract: Abstract 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. Graphical abstract

Date: 2024
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DOI: 10.1140/epjb/s10051-023-00645-5

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