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Stochastic resonance in a harmonic oscillator with fractional-order external and intrinsic dampings

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Abstract

In this paper, the phenomenon of stochastic resonance (SR) in a harmonic oscillator with fractional-order external and intrinsic dampings under the external periodic force is investigated. Applying the Shapiro–Loginov formula, fractional Shapiro–Loginov formula, generalized fractional Shapiro–Loginov formula and the Laplace transform technique, we obtain the analytic expressions of the first moment and the amplitude of the output signal. By studying the impacts of the driving frequency, system parameters and the noise parameters, we find the non-monotonic behaviors of the output amplitude. The results indicate that the bona fide SR, the generalized SR and the conventional SR phenomena occur in the proposed model. Furthermore, the numerical simulations are presented to verify the effectiveness of the analytic result.

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Acknowledgments

This work was supported by the Key Program of National Natural Science Foundation of China (Grant Number 11171238), Natural Science Foundation for the Youth (Grant Number 11401405) and the Young Teacher Fund of Sichuan University, China (Grant Number 2082604174031).

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Authors and Affiliations

  1. College of Aeronautics and Astronautics, Sichuan University, Chengdu, 610065, China

    Suchuan Zhong

  2. College of Mathematics, Sichuan University, Chengdu, 610065, China

    Hong Ma & Lu Zhang

  3. College of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China

    Hao Peng

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  1. Suchuan Zhong
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  2. Hong Ma
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  3. Hao Peng
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  4. Lu Zhang
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Correspondence to Suchuan Zhong.

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Zhong, S., Ma, H., Peng, H. et al. Stochastic resonance in a harmonic oscillator with fractional-order external and intrinsic dampings. Nonlinear Dyn 82, 535–545 (2015). https://doi.org/10.1007/s11071-015-2174-2

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  • DOI: https://doi.org/10.1007/s11071-015-2174-2

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