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Unsaturated piecewise bistable stochastic resonance with three kinds of asymmetries and time-delayed feedback

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  • Ma, Tianchi
  • Song, Di
  • Shen, Junxian
  • Xu, Feiyun

Abstract

The performance of an unsaturated piecewise bistable stochastic resonance (UPBSR) with three kinds of asymmetries and time-delayed feedback is investigated. Firstly, by introducing an asymmetric factor into UPBSR potential, three kinds of asymmetries are constructed, i.e., well-depth asymmetry (WDA), well-width asymmetry (WWA), and both well-depth and well-width asymmetry (BDWA). Then, by using two-state theory and small delay approximation, the output signal-to-noise ratio (SNR) is derived to analyze the behavior of SR. Enhancement ability and noise immunity are adopted as SR evaluation index. Moreover, as an intermediate result in the calculation of the SNR, the mean first passage time (MFPT), is often used to discuss the transient properties of nonlinear systems. Finally, for SNR analysis, the results show that asymmetric SR outperforms symmetric SR when the asymmetric factor is in the appropriate range, and the WDA dominates the three cases. In addition, the effect of feedback intensity on SR depends heavily on the asymmetric cases, it plays the opposite role in different asymmetric cases. In contrast, the effect of time delay is independent on the asymmetric cases, which always exhibits an improvement of SR noise immunity. As for MFPT analysis, the small γ and β are conducive to the transition of the particles between potential wells, while τ almost has no effect on the transition of particles.

Suggested Citation

  • Ma, Tianchi & Song, Di & Shen, Junxian & Xu, Feiyun, 2022. "Unsaturated piecewise bistable stochastic resonance with three kinds of asymmetries and time-delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005628
    DOI: 10.1016/j.chaos.2022.112352
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    References listed on IDEAS

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    1. Liu, Jian & Wang, Youguo, 2018. "Performance investigation of stochastic resonance in bistable systems with time-delayed feedback and three types of asymmetries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 359-369.
    2. M. Gosak & M. Perc & S. Kralj, 2011. "Stochastic resonance in a locally excited system of bistable oscillators," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 80(4), pages 519-528, April.
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    Cited by:

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    2. 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).

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