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Noise-induced resonance at the subharmonic frequency in bistable systems

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Abstract

In a bistable system excited by the combination of a weak low-frequency signal and a noise, the noise can induce a resonance at the subharmonic frequency which is smaller than the driving frequency. This kind of noise-induced resonance is similar to the well-known stochastic resonance. Here, we verify the noise-induced resonance at the subharmonic frequency which equals 1/3 multiple of the driving frequency, by a numerical study of the response of the overdamped and underdamped bistable systems, respectively. More importantly, the noise-induced resonance at the subharmonic frequency may be stronger than the classical stochastic resonance which occurs at the driving frequency. This indicates that we cannot ignore the subharmonic frequency component in the response, otherwise we may miss some important information. By adjusting the excitation signal and the system parameters, we can make the noise-induced resonance at the subharmonic frequency to be stronger or weaker than the classic stochastic resonance. The results shown in this paper constitute a complement to the stochastic dynamics of a random system.

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Author information

Authors and Affiliations

  1. School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou, 221116, China

    J. H. Yang, H. G. Liu & H. Zhu

  2. Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, China University of Mining and Technology, Xuzhou, 221116, China

    J. H. Yang, H. G. Liu & H. Zhu

  3. Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933, Móstoles, Madrid, Spain

    Miguel A. F. Sanjuán

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  1. J. H. Yang
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  2. Miguel A. F. Sanjuán
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  3. H. G. Liu
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  4. H. Zhu
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Correspondence to J. H. Yang.

Additional information

The work is supported by the National Natural Science Foundation of China (Grant Nos. 11672325, 51305441, 51375480), the Priority Academic Program Development of Jiangsu Higher Education Institutions, the Top-notch Academic Programs Project of Jiangsu Higher Education Institutions, and the Spanish Ministry of Science and Innovation (Grant No. FIS2009-09898). We thank professor Canjun Wang in Baoji University of Arts and Sciences for the useful discussions. We are grateful to the anonymous reviewers for their valuable comments and advice, which are vital for improving the quality of this paper.

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Yang, J.H., Sanjuán , M.A.F., Liu, H.G. et al. Noise-induced resonance at the subharmonic frequency in bistable systems. Nonlinear Dyn 87, 1721–1730 (2017). https://doi.org/10.1007/s11071-016-3147-9

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  • DOI: https://doi.org/10.1007/s11071-016-3147-9

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