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Coherence resonance in fractional van der Pol oscillators

  • Regular Article-Statistical and Nonlinear Physics
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Abstract

The phenomenon of coherence resonance (CR) in two typical kinds of fractional van del Pol oscillator is investigated. For the first model, the damping term of the ordinary van der Pol oscillator is replaced by a fractional-order damping. While in the second model, the fractional-order damping is instead of the inertia term of the ordinary van der Pol oscillator. In the first model, there is obvious CR by adjusting the noise intensity. The resonance frequency mainly depends on the value of the fractional-order but it is almost independent of the noise intensity when the noise intensity is small, but change with the noise intensity when the noise intensity lies in a slightly large range. However, the resonance frequency of the ordinary van der Pol oscillator does not influence by the noise. In addition, with the increase of the fractional-order, the resonance frequency decreases monotonicity. Whereas, the resonance amplitude is a nonmonotonic function of the fractional-order. When the fractional oscillator deviates from the ordinary one, the resonance amplitude is much greater. In the second model, CR occurs only when the fractional oscillator is very close to the ordinary van der Pol oscillator. Comparing CR in the first model with that in the second model, we find that the value of the fractional-order can be taken over a much larger range to induce CR for the first one. The study shows that the inertia term is an indispensable factor in causing CR phenomenon while the fractional-order damping only changes the resonance frequency in different kinds of van der Pol oscillators.

Graphic abstract

Coherence resonance phenomenon in the fractional van der Pol oscillator under different values of the fractional-order and noise intensity.

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Data Availability Statement

All data included in this manuscript are available upon request by contacting with the corresponding author.

References

  1. L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70(1), 223 (1998)

    Article  ADS  Google Scholar 

  2. H. Gang, T. Ditzinger, C.Z. Ning, H. Haken, Phys. Rev. Lett. 71(6), 807 (1993)

    Article  ADS  Google Scholar 

  3. A. Pikovsky, J. Kurths, Phys. Rev. Lett. 78(5), 775 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  4. Y. Wang, D.T. Chik, Z.D. Wang, Phys. Rev. E 61(1), 740 (2000)

    Article  ADS  Google Scholar 

  5. C. Zhou, J. Kurths, Chaos 13(1), 401 (2003)

    Article  ADS  Google Scholar 

  6. J. Casado, Phys. Lett. A 235(5), 489 (1997)

    Article  ADS  Google Scholar 

  7. N.B. Janson, A.G. Balanov, E. Schöll, Phys. Rev. Lett. 93(1), 010601 (2004)

    Article  ADS  Google Scholar 

  8. A.G. Balanov, N.B. Janson, E. Schöll, Phys. D 199(1–2), 1 (2004)

    Article  Google Scholar 

  9. X.Y. Li, J.H. Yang, X.B. Liu, Fluct. Noise Lett. 11(2), 125002 (2012)

    Article  Google Scholar 

  10. A.N. Pisarchik, A.E. Hramov, Phys. Rep. 1000, 1 (2023)

    Article  MathSciNet  ADS  Google Scholar 

  11. Z.H. Hou, H.W. Xin, Phys. Rev. E 60(6), 6329 (1999)

    Article  ADS  Google Scholar 

  12. J. Ma, T. Xiao, Z. Hou, H. Xin, Chaos 18(4), 043116 (2008)

    Article  ADS  Google Scholar 

  13. J. Ma, Z.H. Hou, H.W. Xin, Eur. Phys. J. B. 69, 101 (2009)

    Article  ADS  Google Scholar 

  14. C.A. Monje, Y. Chen, B.M. Vinagre, D. Xue, V. Feliu, Fractional-order Systems and Controls (Springer, London, 2010)

    Book  Google Scholar 

  15. M.A. Khan, S. Ullah, S. Kumar, Eur. Phys. J. Plus 136, 1 (2021)

    Article  Google Scholar 

  16. S. Kumar, R.P. Chauhan, S. Momani, S. Hadid, Numer. Meth. Part. D. E. 40(1), e22707 (2024)

    Article  Google Scholar 

  17. S. Kumar, R. Kumar, S. Momani, S. Hadid, Math. Method. Appl. Sci. 46(7), 7671 (2023)

    Article  ADS  Google Scholar 

  18. M. Di Paola, R. Heuer, A. Pirrotta, Int. J. Solids Struct. 50(22–23), 3505 (2013)

    Article  Google Scholar 

  19. W. Sumelka, T. Blaszczyk, C. Liebold, Eur. J. Mech. A Solid. 54, 243 (2015)

    Article  ADS  Google Scholar 

  20. Y. Zhang, X. Liu, M.R. Belić, W. Zhong, Y. Zhang, M. Xiao, Phys. Rev. Lett. 115(18), 180403 (2015)

    Article  ADS  Google Scholar 

  21. S. Kumar, A. Kumar, B. Samet, H. Dutta, Numer. Meth. Part. D. E. 37(2), 1673 (2021)

    Article  Google Scholar 

  22. B. Ghanbari, S. Kumar, Numer. Meth. Part. D E 40(1), e22689 (2024)

    Article  Google Scholar 

  23. P. Veeresha, D.G. Prakasha, S. Kumar, Math. Method. Appl. Sci. (2020). https://doi.org/10.1002/mma.6335

    Article  Google Scholar 

  24. S. Das, I. Pan, Fractional Order Signal Processing: Introductory Concepts and Applications (Springer Science & Business Media, Berlin, 2011)

    Google Scholar 

  25. R. Magin, M.D. Ortigueira, I. Podlubny, J. Trujillo, Signal Process. 91(3), 350 (2011)

    Article  Google Scholar 

  26. F. Pourdadashi-Komachali, M. Shafiee, Int. J. Syst. Sci. 51(1), 116 (2020)

    Article  Google Scholar 

  27. C. Wu, J. Yang, D. Huang, H. Liu, E. Hu, Meas. Sci. Technol. 30(3), 035004 (2019)

    Article  ADS  Google Scholar 

  28. A.Y.T. Leung, H.X. Yang, Z.J. Guo, J. Sound Vib. 331(5), 1115 (2012)

    Article  ADS  Google Scholar 

  29. Z. Guo, A.Y.T. Leung, H.X. Yang, Appl. Math. Model. 35(8), 3918 (2011)

    Article  MathSciNet  Google Scholar 

  30. N. Van Khang, B.T. Thuy, T.Q. Chien, J. Comput. Nonlin. Dyn. 11(4), 041030 (2016)

    Article  Google Scholar 

  31. L. Chen, H. Li, Z. Li, W. Zhu, Sci. China Phys. Mech. 56, 2200 (2013)

    Article  Google Scholar 

  32. Y. Shen, S. Yang, C. Sui, Chaos Soliton. Fract. 67, 94 (2014)

    Article  ADS  Google Scholar 

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Acknowledgements

The project was supported by the National Natural Science Foundation of China (Grant Nos. 12072362), the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, People’s Republic of China

    Shangyuan Li, Chenhang Hao & Jianhua Yang

  2. School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, People’s Republic of China

    Zhongqiu Wang

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  1. Shangyuan Li
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  2. Zhongqiu Wang
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Correspondence to Zhongqiu Wang.

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Li, S., Wang, Z., Hao, C. et al. Coherence resonance in fractional van der Pol oscillators. Eur. Phys. J. B 97, 47 (2024). https://doi.org/10.1140/epjb/s10051-024-00684-6

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