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Simple megastable oscillators with different types of attractors; tori, chaotic and hyperchaotic ones

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Abstract

Coexistence of attractors with different or same type, multistability, is a complex behavior in nonlinear systems. This feature makes these systems applicable but difficult to control. Besides multistability, some new systems show megastability, existence of infinite number of coexisting attractors. In this paper, two simple megastable systems are presented in details. Moreover, these systems show hyperchaotic behavior which is rare in these types of systems as previously proposed systems mostly show chaos and periodic responses. To show the properties of these systems, nonlinear analytical tools are used in this article.

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References

  1. D. Patil, B.R. Hunt, E. Kalnay, J.A. Yorke, E. Ott, Phys. Rev. Lett. 86, 5878 (2001)

    ADS  Google Scholar 

  2. S.J. Schiff, K. Jerger, D.H. Duong, T. Chang, M.L. Spano, W.L. Ditto, Nature 370, 615 (1994)

    ADS  Google Scholar 

  3. D.W. Crevier, M. Meister, J. Neurophysiol. 79, 1869 (1998)

    Google Scholar 

  4. D. Peng, K. Sun, S. He, L. Zhang, A.O. Alamodi, Theor. Appl. Mech. Lett. 9, 220 (2019)

    Google Scholar 

  5. S. Jafari, J.C. Sprott, Chaos Solitons Fractals 57, 79 (2013)

    ADS  MathSciNet  Google Scholar 

  6. T. Gotthans, J.C. Sprott, J. Petrzela, Int. J. Bifurc. Chaos 26, 1650137 (2016)

    Google Scholar 

  7. G. Leonov, N. Kuznetsov, V. Vagaitsev, Phys. Lett. A 375, 2230 (2011)

    ADS  MathSciNet  Google Scholar 

  8. G. Leonov, N. Kuznetsov, V. Vagaitsev, Physica D 241, 1482 (2012)

    ADS  MathSciNet  Google Scholar 

  9. N. Kuznetsov, G. Leonov, M. Yuldashev, R. Yuldashev, Commun. Nonlinear Sci. Numer. Simul. 51, 39 (2017)

    ADS  Google Scholar 

  10. S. He, K. Sun, C.X. Zhu, Chin. Phys. B 22, 050506 (2013)

    ADS  Google Scholar 

  11. Y. Peng, K. Sun, S. He, D. Peng, Entropy 21, 27 (2019)

    ADS  Google Scholar 

  12. Y. Peng, K. Sun, S. He, O. Alamodi, Mod. Phys. Lett. B 33, 1950041 (2019)

    ADS  Google Scholar 

  13. D. Peng, K. Sun, S. He, A.O. Alamodi, Chaos Solitons Fractals 119, 163 (2019)

    ADS  MathSciNet  Google Scholar 

  14. X. Li, B. Liu, J. Wu, IEEE Trans. Autom. Control 63, 306 (2016)

    ADS  Google Scholar 

  15. X. Li, X. Fu, J. Franklin Inst. 350, 1335 (2013)

    MathSciNet  Google Scholar 

  16. D. Angeli, J.E. Ferrell, E.D. Sontag, Proc. Natl. Acad. Sci. USA 101, 1822 (2004)

    ADS  Google Scholar 

  17. D.A. Prousalis, C.K. Volos, B. Bao, E. Meletlidou, I.N. Stouboulos, I.M. Kyprianidis, in Extreme multistability in a hyperjerk memristive system with hidden attractors. Recent advances in chaotic systems and synchronization, (Elsevier, 2019), pp. 89–103

  18. Y. Zhang, Z. Liu, H. Wu, S. Chen, B. Bao, Chaos Solitons Fractals 127, 354 (2019)

    ADS  MathSciNet  Google Scholar 

  19. H. Bao, N. Wang, B. Bao, M. Chen, P. Jin, G. Wang, Commun. Nonlinear Sci. Numer. Simul. 57, 264 (2018)

    ADS  MathSciNet  Google Scholar 

  20. J.C. Sprott, S. Jafari, A.J.M. Khalaf, T. Kapitaniak, Eur. Phys. J. Special Topics 226, 1979 (2017)

    ADS  Google Scholar 

  21. R. Calov, A. Ganopolski, Geophys. Res. Lett. 32, L21717 (2005)

    ADS  Google Scholar 

  22. X. Zhang, X. Lv, X. Li, Nonlinear Dyn. 90, 2199 (2017)

    Google Scholar 

  23. D. Angeli, J.E. Ferrell, E.D. Sontag, Proc. Natl. Acad. Sci. 101, 1822 (2004)

    ADS  Google Scholar 

  24. M. Laurent, N. Kellershohn, Trends Biochem. Sci. 24, 418 (1999)

    Google Scholar 

  25. B. Bao, H. Bao, N. Wang, M. Chen, Q. Xu, Chaos Solitons Fractals 94, 102 (2017)

    ADS  MathSciNet  Google Scholar 

  26. B. Bao, Q. Li, N. Wang, Q. Xu, Chaos 26, 043111 (2016)

    ADS  MathSciNet  Google Scholar 

  27. A.N. Pisarchik, U. Feudel, Phys. Rep. 540, 167 (2014)

    ADS  MathSciNet  Google Scholar 

  28. P. Sharma, M. Shrimali, A. Prasad, N. Kuznetsov, G. Leonov, Eur. Phys. J. Special Topics 224, 1485 (2015)

    ADS  Google Scholar 

  29. S. He, C. Li, K. Sun, S. Jafari, Entropy 20, 556 (2018)

    ADS  Google Scholar 

  30. Z. Wei, V.T. Pham, A.J.M. Khalaf, V. Kengne, S. Jafari, Int. J. Bifurc. Chaos 28, 1850085 (2018)

    Google Scholar 

  31. A.J.M.K. Yan-Xia Tang, K. Rajagopal, V.T. Pham, S. Jafari, Y. Tian, Chin. Phys. B. 27, 40502 (2018)

    Google Scholar 

  32. S. Jafari, A. Ahmadi, S. Panahi, K. Rajagopal, Chaos Solitons Fractals 108, 182 (2018)

    ADS  Google Scholar 

  33. S. Jafari, A. Ahmadi, A.J.M. Khalaf, H.R. Abdolmohammadi, V.T. Pham, , AEU Int. J. Electron. Commun. 89, 131 (2018)

    Google Scholar 

  34. N. Kuznetsov, T. Mokaev, P. Vasilyev, Commun. Nonlinear Sci. Numer. Simul. 19, 1027 (2014)

    ADS  MathSciNet  Google Scholar 

  35. N. Kuznetsov, Phys. Lett. A 380, 2142 (2016)

    ADS  MathSciNet  Google Scholar 

  36. A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985)

    ADS  MathSciNet  Google Scholar 

  37. C. Li, J.C. Sprott, Phys. Lett. A 382, 581 (2018)

    ADS  MathSciNet  Google Scholar 

  38. C. Li, J.C. Sprott, W. Hu, Y. Xu, Int. J. Bifurc. Chaos 27, 1750160 (2017)

    Google Scholar 

  39. C. Li, J.C. Sprott, Y. Mei, Nonlinear Dyn. 89, 2629 (2017)

    Google Scholar 

  40. X. Li, X. Zhang, S. Song, Automatica 76, 378 (2017)

    Google Scholar 

  41. J. Tao, R. Lu, H. Su, Z.G. Wu, IEEE Trans. Syst. Man Cybern. Syst. 48, 2442 (2017)

    Google Scholar 

  42. P. Prakash, K. Rajagopal, J. Singh, B. Roy, AEU Int. J. Electron. Commun. 92, 111 (2018)

    Google Scholar 

  43. K. Rajagopal, J.P. Singh, B.K. Roy, A. Karthikeyan, Chin. J. Phys. 58, 263 (2019)

    Google Scholar 

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Authors and Affiliations

  1. School of Electronic Engineering, Changzhou College of Information Technology, Wujin, 213164, P.R. China

    Biqun Chen & Anitha Karthikeyan

  2. Center for Nonlinear Dynamics, Defence University, Bishoftu, Ethiopia

    Karthikeyan Rajagopal

  3. Department of Computer Science and Engineering, University of Kurdistan-Hewler, Erbil, Iraq

    Ibrahim Ismael Hamarash

  4. Department of Mathematics, Statistics and Physics, Qatar University, Doha, 2713, Qatar

    Iqtadar Hussain

Authors
  1. Biqun Chen
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  2. Karthikeyan Rajagopal
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  3. Ibrahim Ismael Hamarash
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  4. Anitha Karthikeyan
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  5. Iqtadar Hussain
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Correspondence to Karthikeyan Rajagopal.

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Chen, B., Rajagopal, K., Hamarash, I.I. et al. Simple megastable oscillators with different types of attractors; tori, chaotic and hyperchaotic ones. Eur. Phys. J. Spec. Top. 229, 1155–1161 (2020). https://doi.org/10.1140/epjst/e2020-900240-1

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  • DOI: https://doi.org/10.1140/epjst/e2020-900240-1

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