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Stochastic resonance in multi-stable coupled systems driven by two driving signals

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  • Xu, Pengfei
  • Jin, Yanfei

Abstract

The stochastic resonance (SR) in multi-stable coupled systems subjected to Gaussian white noises and two different driving signals is investigated in this paper. Using the adiabatic approximation and the perturbation method, the coupled systems with four-well potential are transformed into the master equations and the amplitude of the response is obtained. The signal-to-noise ratio (SNR) is calculated numerically to demonstrate the occurrence of SR. For the case of two driving signals with different amplitudes, the interwell resonance between two wells S1 and S3 emerges for strong coupling. The SR can appear in the subsystem with weaker signal amplitude or even without driving signal with the help of coupling. For the case of two driving signals with different frequencies, the effects of SR in two subsystems driven by high and low frequency signals are both weakened with an increase in coupling strength. The stochastic multi-resonance phenomenon is observed in the subsystem subjected to the low frequency signal. Moreover, an effective scheme for phase suppressing SR is proposed by using a relative phase between two driving signals.

Suggested Citation

  • Xu, Pengfei & Jin, Yanfei, 2018. "Stochastic resonance in multi-stable coupled systems driven by two driving signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1281-1289.
    • Handle: RePEc:eee:phsmap:v:492:y:2018:i:c:p:1281-1289
    DOI: 10.1016/j.physa.2017.11.056
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    Citations

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    Cited by:

    1. Zhu, Jinjie & Zhao, Feng & Li, Yang & Liu, Xianbin, 2024. "Rotational stochastic resonance in multistable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).
    2. Zhang, Gang & Chen, Yezi & Xu, Lianbing, 2024. "Multi-dimensional hybrid potential stochastic resonance and application of bearing fault diagnosis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).
    3. He, Lifang & Jiang, Zhiyuan & Chen, Yezi, 2024. "Unveiling the principles of stochastic resonance and complex potential functions for bearing fault diagnosis," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    4. Xu, Pengfei & Jin, Yanfei & Zhang, Yanxia, 2019. "Stochastic resonance in an underdamped triple-well potential system," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 352-362.
    5. Gong, Xulu & Xu, Pengfei & Liu, Di & Zhou, Biliu, 2023. "Stochastic resonance of multi-stable energy harvesting system with high-order stiffness from rotational environment," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Hollerbach, Rainer & Kim, Eun-jin & Mahi, Yanis, 2019. "Information length as a new diagnostic in the periodically modulated double-well model of stochastic resonance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1313-1322.
    7. He, Lifang & Wu, Xia & Zhang, Gang, 2020. "Stochastic resonance in coupled fractional-order linear harmonic oscillators with damping fluctuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    8. Bi, Haohao & Lei, Youming & Han, Yanyan, 2019. "Stochastic resonance across bifurcations in an asymmetric system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1296-1312.
    9. Zhang, Gang & Liu, Xiaoman & Zhang, Tianqi, 2022. "Two-Dimensional Tri-stable Stochastic Resonance system and its application in bearing fault detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).

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