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A system governed by a set of nonautonomous differential equations with robust strange nonchaotic attractor of Hunt and Ott type

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Abstract

A physically realizable nonautonomous system of ring structure is considered, which manifests a robust strange nonchaotic attractor (SNA), similar to the attractor in the map on a torus proposed earlier by Hunt and Ott. Numerical simulation of the dynamics for the corresponding non-autonomous set of differential equations with quasi-periodic coefficients is provided. It is demonstrated that in terms of appropriately chosen phase variables the dynamics is consistent with the topology of the mapping of Hunt and Ott on the characteristic period. It has been shown that the occurrence of SNA agrees with the criterion of Pikovsky and Feudel. Also, the computations confirm that the Fourier spectrum in sustained SNA mode is of intermediate class between the continuous and discrete spectra (the singular continuous spectrum).

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References

  1. C. Grebogi, E. Ott, S. Pelikan, J.A. Yorke, Physica D 13, 261 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  2. U. Feudel, S. Kuznetsov, A. Pikovsky, Strange Nonchaotic Attractors. Dynamics between Order and Chaos in Quasiperiodically Forced Systems (World Scientific, Singapore, 2006), p. 228

  3. A. Bondeson, E. Ott, T.M. Antonsen, Phys. Rev. Lett. 55, 2103 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  4. M. Ding, C. Grebogi, E. Ott, Phys. Lett. A 137, 167 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  5. M. Ding, C. Grebogi, E. Ott, Phys. Rev. A 39, 2593 (1989)

    Article  ADS  Google Scholar 

  6. A.S. Pikovsky, U. Feudel, J. Phys. A: Math. Gen. 27, 5209 (1994)

    Article  ADS  Google Scholar 

  7. A.S. Pikovsky, U. Feudel, Chaos 5, 253 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  8. A.S. Pikovsky, M.A. Zaks, U. Feudel, J. Kurths, Phys. Rev. E 52, 285 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  9. U. Feudel, A.S. Pikovsky, J. Kurths, Physica D 88, 176 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  10. P. Pokorny, I. Schreiber, M. Marek, Chaos, Solitons and Fractals 7, 409 (1996)

    Article  ADS  MATH  Google Scholar 

  11. K. Kaneko, T. Nishikawa, Phys. Rev. E 54, 6114 (1996)

    Article  ADS  Google Scholar 

  12. P. Glendinning, Phys. Lett. A 244, 545 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  13. H. Osinga, J. Wiersig, P. Glendinning, U. Feudel, Int. J. Bifurc. Chaos 11, 3085 (2001)

    Article  Google Scholar 

  14. A. Prasad, S.S. Negi, R. Ramaswamy, Int. J. Bifurc. Chaos 11, 291 (2001)

    Article  Google Scholar 

  15. B.R. Hunt, E. Ott, Phys. Rev. Lett. 87, 254101 (2001)

    Article  ADS  Google Scholar 

  16. J.-W. Kim, S.-Y. Kim, B. Hunt, E. Ott, Phys. Rev. E 67, 036211 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  17. S.-Y. Kim, W. Lim, E. Ott, Phys. Rev. E 67, 056203 (2003)

    Article  ADS  Google Scholar 

  18. A.Yu. Jalnine, S.P. Kuznetsov, EPL 115, 30004 (2016)

    Article  ADS  Google Scholar 

  19. W.L. Ditto, M.L. Spano, H.T. Savage, S.N. Rauseo, J. Heagy, E. Ott, Phys. Rev. Lett. 65, 533 (1990)

    Article  ADS  Google Scholar 

  20. S.T. Vohra, F. Bucholtz, K.P. Koo, D.M. Dagenais, Phys. Rev. Lett. 66, 212 (1991)

    Article  ADS  Google Scholar 

  21. T. Zhou, F. Moss, A. Bulsara, Phys. Rev. A 45, 5394 (1992)

    Article  ADS  Google Scholar 

  22. K.-P. Zeyer, A.F. Miinster, F.W. Schneider, J. Phys. Chem. 99, 13173 (1995)

    Article  Google Scholar 

  23. W.X. Ding, H. Deutsch, A. Dinklage, C. Wilke, Phys. Rev. E 55, 3769 (1997)

    Article  ADS  Google Scholar 

  24. T. Yang, K. Bilimgut, Phys. Lett. A 236, 494 (1997)

    Article  ADS  Google Scholar 

  25. Y.H. Yu, D.C. Kim, J.Y. Ryu, S.R. Hong, J. Korean Phys. Soc. 34, 130 (1999)

    Google Scholar 

  26. B.P. Bezruchko, S.P. Kuznetsov, Y.P. Seleznev, Phys. Rev. E 62, 7828 (2000)

    Article  ADS  Google Scholar 

  27. D. Sanchez, G. Platero, L.L. Bonilla, Phys. Rev. B 63, 201306 (2001)

    Article  ADS  Google Scholar 

  28. A. Vaszlenko, O. Feely, Int. J. Bifurc. Chaos 12, 1633 (2002)

    Article  Google Scholar 

  29. A.Yu. Jalnine, S.P. Kuznetsov, Tech. Phys. 52, 401 (2007)

    Article  Google Scholar 

  30. G. Benettin, L. Galgani, A. Giorgilli, J.M. Strelcyn, Meccanica 15, 9 (1980)

    Article  ADS  Google Scholar 

  31. S.P. Kuznetsov, Hyperbolic Chaos: A Physicist’s View (Higher Education Press: Beijing, Springer-Verlag: Berlin, Heidelberg, 2012), p. 336

  32. A. Pikovsky, A. Politi, Lyapunov Exponents: A Tool to Explore Complex Dynamics (Cambridge University Press, 2016), p. 285

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Authors and Affiliations

  1. Chernyshevsky Saratov State University, Astrakhanskaya, 83, Saratov, 410012, Russia

    Valentina M. Doroshenko & Sergey P. Kuznetsov

  2. Kotelnikov Institute of Radio-Engineering and Electronics, Saratov Branch, Zelenaya, 38, Saratov, 410019, Russia

    Sergey P. Kuznetsov

Authors
  1. Valentina M. Doroshenko
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  2. Sergey P. Kuznetsov
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Correspondence to Valentina M. Doroshenko or Sergey P. Kuznetsov.

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Doroshenko, V.M., Kuznetsov, S.P. A system governed by a set of nonautonomous differential equations with robust strange nonchaotic attractor of Hunt and Ott type. Eur. Phys. J. Spec. Top. 226, 1765–1775 (2017). https://doi.org/10.1140/epjst/e2017-70041-y

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  • DOI: https://doi.org/10.1140/epjst/e2017-70041-y

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