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Stochastic resonance in an underdamped triple-well potential system

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  • Xu, Pengfei
  • Jin, Yanfei
  • Zhang, Yanxia

Abstract

In this paper, stochastic resonance (SR) in an underdamped triple-well potential system driven by Gaussian white noise and a parametric harmonic excitation is investigated. The analytical expressions of the output signal-to-noise ratio (SNR), together with the mean first-passage times (MFPTs), are derived for the triple-well potential system involving damping in adiabatic limit. The effects of noise intensity, damping coefficient and triple-well potential on MFPTs and SNR are analyzed. The results suggest the existence of two critical damping values, giving rise to the onset and the disappearance of SR, respectively. Since the system is unstable in weak damping regime, emergence of SR is prohibited. Under the weak noise level, SNR exhibits a prominent resonance-like behavior at the optimal value of damping coefficient. Moreover, the two nonlinear stiffness coefficients of restoring force play an opposite role in the enhancement of SR. Thus, the SR effect significantly depends on the change of the two-side potential wells. Particularly, the appropriate choice of triple-well potential function and damping coefficient can improve the response of the system to an external periodic excitation according to the damping-induced resonance effect. Finally, the numerical results confirm the effectiveness of the theoretical analyses.

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  • 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.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:352-362
    DOI: 10.1016/j.amc.2018.10.060
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    References listed on IDEAS

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    1. Xu, Pengfei & Jin, Yanfei, 2018. "Mean first-passage time in a delayed tristable system driven by correlated multiplicative and additive white noises," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 75-82.
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    5. Yilmaz, Ergin & Uzuntarla, Muhammet & Ozer, Mahmut & Perc, Matjaž, 2013. "Stochastic resonance in hybrid scale-free neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5735-5741.
    6. Zhou, Shengxi & Cao, Junyi & Inman, Daniel J. & Lin, Jing & Liu, Shengsheng & Wang, Zezhou, 2014. "Broadband tristable energy harvester: Modeling and experiment verification," Applied Energy, Elsevier, vol. 133(C), pages 33-39.
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    Cited by:

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    2. 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).
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    5. Xu, Pengfei & Gong, Xulu & Wang, Haotian & Li, Yiwei & Liu, Di, 2023. "A study of stochastic resonance in tri-stable generalized Langevin system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    6. Xu, Pengfei & Jin, Yanfei, 2020. "Coherence and stochastic resonance in a second-order asymmetric tri-stable system with memory effects," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    7. Dongmei Huang & Shengxi Zhou & Zhichun Yang, 2019. "Resonance Mechanism of Nonlinear Vibrational Multistable Energy Harvesters under Narrow-Band Stochastic Parametric Excitations," Complexity, Hindawi, vol. 2019, pages 1-20, December.

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