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<p>The vibrational resonance (VR) and stochastic resonance (SR) for a second-order fractional-damping bistable system driven by one high-frequency (HF) and one low-frequency (LF) periodic signal subjected to multiplicative and additive noise are investigated. By decomposing the system output signal into one LF motion and one HF motion, based on two-state theory, the system output signal-to-noise ratio (SNR) for the LF signal is deduced. It is found that double bona fide VR and bona fide SR phenomena take place when the SNR varies respectively with the frequency of the HF signal and with the frequency of the LF signal. VR appears when the SNR changes with the amplitude of the HF signal. One resonance peak occurs when the SNR changes with the fractional exponent. The SNR exhibits resonance behavior for an appropriate amount of multiplicative noise. Moreover, the influence of the amplitude and frequency of the HF signal on the SNR is different.</p>

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Resonance phenomenon for a second-order fractional-damping bistable system with high-frequency and low-frequency periodic signals

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • Qiang-Ming Cai,
  • Yu-Rui Jia,
  • Long-Jian Zhou,
  • Xin Cao,
  • Feng Guo

摘要

The vibrational resonance (VR) and stochastic resonance (SR) for a second-order fractional-damping bistable system driven by one high-frequency (HF) and one low-frequency (LF) periodic signal subjected to multiplicative and additive noise are investigated. By decomposing the system output signal into one LF motion and one HF motion, based on two-state theory, the system output signal-to-noise ratio (SNR) for the LF signal is deduced. It is found that double bona fide VR and bona fide SR phenomena take place when the SNR varies respectively with the frequency of the HF signal and with the frequency of the LF signal. VR appears when the SNR changes with the amplitude of the HF signal. One resonance peak occurs when the SNR changes with the fractional exponent. The SNR exhibits resonance behavior for an appropriate amount of multiplicative noise. Moreover, the influence of the amplitude and frequency of the HF signal on the SNR is different.