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Self-oscillations in a system with hysteresis: the small parameter approach

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Abstract

The paper investigates a modified van der Pol equation with hysteresis nonlinearity which is formalized within the Preisach approach. The system considered in the work is a mathematical model of an electrical system similar to the classical van der Pol system where characteristics of the nonlinear part are of hysteresis nature. The main method for studying this system is the classical small parameter approach. Within this method, an analytical solution to the equation describing the system under consideration was obtained. Numerical results are presented and a comparative analysis of the dynamics of the system under consideration with the dynamics of the classical van der Pol oscillator is carried out. Dynamic modes of the modified oscillator are investigated depending on the parameters of the system. Spectral characteristics are also compared to the corresponding characteristics of the classical van der Pol oscillator.

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Acknowledgements

This work was supported by the RFBR (Grant 19-08-00158). The contributions by M.E. Semenov and P.A. Meleshenko (Section: Model) were supported by the RSF grant No. 19-11-00197.

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Authors and Affiliations

  1. Voronezh State University, Universitetskaya sq. 1, 394018, Voronezh, Russia

    Mikhail E. Semenov, Olga O. Reshetova, Sergey V. Borzunov & Peter A. Meleshenko

  2. Geophysical Survey of Russia Academy of Science, Lenina av. 189, 249035, Obninsk, Russia

    Mikhail E. Semenov

  3. Voronezh State Technical University, XX-letiya Oktyabrya st. 84, 394006, Voronezh, Russia

    Mikhail E. Semenov

  4. Zhukovsky-Gagarin Air Force Academy, Starykh Bolshevikov st. 54 “A”, 394006, Voronezh, Russia

    Mikhail E. Semenov

  5. Target Search Lab of Groundbreaking Radio Communication Technologies of Advanced Research Foundation, Bld. 1, Shokin Square, 124498, Zelenograd, Moscow, Russia

    Peter A. Meleshenko

Authors
  1. Mikhail E. Semenov
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  2. Olga O. Reshetova
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  3. Sergey V. Borzunov
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  4. Peter A. Meleshenko
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Correspondence to Mikhail E. Semenov.

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Semenov, M.E., Reshetova, O.O., Borzunov, S.V. et al. Self-oscillations in a system with hysteresis: the small parameter approach. Eur. Phys. J. Spec. Top. 230, 3565–3571 (2021). https://doi.org/10.1140/epjs/s11734-021-00237-3

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  • DOI: https://doi.org/10.1140/epjs/s11734-021-00237-3

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