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Constructing hyperchaotic attractors of conditional symmetry

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Abstract

By applying the symmetry property of nonlinear function for obtaining new polarity balance, hyperchaotic systems of conditional symmetry are constructed, and coexisting hyperchaotic attractors of conditional symmetry originated from 1-D and 2-D offset boosting are captured accordingly. More interestingly, a symmetric hyperchaotic system is proven to host conditional symmetry, and consequently output coexisting symmetric pair of attractors and their duplication of conditional symmetry. Consequently, two independent processes of attractor merging are observed, which have not been previously reported. Furthermore, the property of offset boosting is discussed for the newly constructed hyperchaotic systems. Circuit implementation based on the develop kit of STM32 is developed, it demonstrates those coexisting attractors are in good agreement with the theoretical analysis and numerical simulations.

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References

  1. O.E. Rössler, Phys. Lett. A 71, 155 (1979)

    ADS  MathSciNet  Google Scholar 

  2. Q. Jia, Phys. Lett. A 366, 217 (2007)

    ADS  Google Scholar 

  3. C. Cao, K. Sun, W. Liu, Signal Process. 143, 122 (2018)

    Google Scholar 

  4. K.P. Harikrishnan, R. Misra, G. Ambika, Eur. Phys. J. B 86, 394 (2013)

    ADS  Google Scholar 

  5. P.C. Rech, Eur. Phys. J. B 90, 251 (2017)

    ADS  Google Scholar 

  6. Q. Lai, A. Akgul, X. Zhao, H. Pei, Int. J. Bifurc. Chaos 27, 1720142 (2017)

    Google Scholar 

  7. S. Pang, Y. Liu, C. Zhu, Comput. Eng. Appl. 49, 235 (2013)

    Google Scholar 

  8. G. Wang, Y. Zhen, J. Liu, Acta Phys. Sin. 56, 3113 (2007)

    Google Scholar 

  9. R. Barboza, Int. J. Bifurc. Chaos 17, 4285 (2007)

    MathSciNet  Google Scholar 

  10. Y. Li, G. Chen, W.K.S. Tang, IEEE Trans. Circuits Syst. II 52, 204 (2005)

    Google Scholar 

  11. C. Shen, S. Yu, J. Lü, G. Chen, IEEE Trans. Circuits Syst. I 61, 854 (2014)

    Google Scholar 

  12. D. Cafagna, G. Grassi, Int. J. Bifurc. Chaos 13, 2889 (2003)

    Google Scholar 

  13. Z. Wang, S. Cang, E.O. Ochola, Y. Sun, Nonlinear Dyn. 69, 531 (2012)

    Google Scholar 

  14. C. Li, J.C. Sprott, Int. J. Bifurc. Chaos 24, 1450034 (2014)

    Google Scholar 

  15. V.T. Pham, F. Rahma, M. Frasca, L. Fortuna, Int. J. Bifurc. Chaos 24, 1450087 (2014)

    Google Scholar 

  16. V.T. Pham, S. Vaidyanathan, C. Volos, S. Jafari, S.T. Kingni, Optik 127, 3259 (2016)

    ADS  Google Scholar 

  17. Z. Wei, R. Wang, A. Liu, Math. Comput. Simul. 100, 13 (2014)

    Google Scholar 

  18. X. Wang, G. Chen, Nonlinear Dyn. 71, 429 (2013)

    Google Scholar 

  19. J. Ma, Z. Chen, Z. Wang, Q. Zhang, Nonlinear Dyn. 81, 1275 (2015)

    Google Scholar 

  20. C. Li, J.C. Sprott, W. Thio, J. Exp. Theor. Phys. 118, 494 (2014)

    ADS  Google Scholar 

  21. G.A. Leonov, V.I. Vagaitsev, N.V. Kuznetsov, Physica D 241, 1482 (2012)

    ADS  MathSciNet  Google Scholar 

  22. G.A. Leonov, N.V. Kuznetsov, Int. J. Bifurc. Chaos 23, 1330002 (2013)

    Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  24. H. Bao, T. Jiang, K. Chu, M. Chen, Q. Xu, B. Bao, Complexity 2018, 5935637 (2018)

    Google Scholar 

  25. L. Zhou, C. Wang, X. Zhang, W. Yao, Int. J. Bifurc. Chaos 28, 1850050 (2018)

    Google Scholar 

  26. Q. Zhao, C. Wang, X. Zhang, Chaos 29, 013141 (2019)

    ADS  MathSciNet  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  28. F. Yuan, G. Wang, X. Wang, Chaos 26, 507 (2016)

    Google Scholar 

  29. C. Li, J.C. Sprott, T. Kapitaniak, T. Lu, Chaos Solitons Fractals 109, 76 (2018)

    ADS  MathSciNet  Google Scholar 

  30. C. Li, A. Akgul, J.C. Sprott, H.H. Lu, W. Thio, Int. J. Circuit Theory Appl. 46, 2434 (2018)

    Google Scholar 

  31. C. Li, J.C. Sprott, H. Xing, Nonlinear Dyn. 87, 1351 (2017)

    Google Scholar 

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

    Google Scholar 

  33. C. Li, Y. Xu, G. Chen, Y. Liu, J. Zheng, Nonlinear Dyn. 95, 1245 (2018)

    Google Scholar 

  34. E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)

    ADS  Google Scholar 

  35. J.C. Sprott, Int. J. Bifurc. Chaos 24, 388 (2014)

    MathSciNet  Google Scholar 

  36. C. Li, W. Hu, J.C. Sprott, X. Wang, Eur. Phys. J. Special Topics 224, 1493 (2015)

    ADS  Google Scholar 

  37. G.M. Chechin, D.S. Ryabov, Phys. Rev. E 69, 036202 (2004)

    ADS  MathSciNet  Google Scholar 

  38. M. Buncha, S. Banlue, Phys. Lett. A 373, 4038 (2009)

    MathSciNet  Google Scholar 

  39. B. Bao, T. Jiang, G. Wang, P. Jin, H. Bao, M. Chen, Nonlinear Dyn. 89, 1157 (2017)

    Google Scholar 

  40. Z. Wei, I. Moroz, J.C. Sprott, A. Akgul, W. Zhang, Chaos 27, 033101 (2017)

    ADS  MathSciNet  Google Scholar 

  41. J.Y. Hsieh, C.C. Hwang, A. Wang, W. Li, Int. J. Control 72, 882 (1999)

    Google Scholar 

  42. X. Wang, X. Wu, Chaos 16, 033121 (2006)

    ADS  Google Scholar 

  43. A. Khan, M.A. Bhat, Int. J. Dyn. Control 5, 1211 (2017)

    MathSciNet  Google Scholar 

  44. C. Li, J.C. Sprott, Optik 127, 10389 (2016)

    ADS  Google Scholar 

  45. C. Li, J.C. Sprott, A. Akgul, H.H. Lu, Y. Zhao, Chaos 27, 083101 (2017)

    ADS  MathSciNet  Google Scholar 

  46. C. Li, X. Wang, G. Chen, Nonlinear Dyn. 90, 1335 (2017)

    Google Scholar 

  47. G.A. Gottwald, L. Melbourne, SIAM J. Appl. Dyn. Syst. 8, 129 (2009)

    ADS  MathSciNet  Google Scholar 

  48. K. Sun, X. Liu, C. Zhu, Chin. Phys. B 19, 110510 (2010)

    ADS  Google Scholar 

  49. L. Zhou, C. Wang, L. Zhou, Nonlinear Dyn. 85, 2653 (2016)

    Google Scholar 

  50. L. Zhou, C. Wang, L. Zhou, Int. J. Circuit Theory Appl. 46, 84 (2018)

    Google Scholar 

  51. C. Wang, X. Liu, H. Xia, Chaos 27, 033114 (2017)

    ADS  Google Scholar 

  52. L. Zhou, C. Wang, L. Zhou, Int. J. Bifurc. Chaos 27, 1750027 (2017)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing, 210044, P.R. China

    Zhenyu Gu, Chunbiao Li & Yibo Zhao

  2. Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science & Technology, Nanjing , 210044, P.R. China

    Zhenyu Gu, Chunbiao Li & Yibo Zhao

  3. School of Electrical, Electronic, and Computing Engineering, The University of Western Australian, 35 Stirling Highway, Crawley, WA, 6009, Australia

    Herbert H. C. Iu

  4. School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, 210042, P.R. China

    Fuhong Min

Authors
  1. Zhenyu Gu
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  2. Chunbiao Li
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  3. Herbert H. C. Iu
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  4. Fuhong Min
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  5. Yibo Zhao
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Contributions

Zhenyu Gu designed hyperchaotic system and explored multistability with circuit implementation. Chunbiao Li launched this project aiming to find hyperchaotic attractors of condtiontional symmetry and proved the results theoretically. Herbert H.C. Iu and Fuhong Min got involved to find different regimes of multistability. Yibo Zhao was involved partially in circuit design and implementation.

Corresponding author

Correspondence to Chunbiao Li.

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Gu, Z., Li, C., Iu, H.H.C. et al. Constructing hyperchaotic attractors of conditional symmetry. Eur. Phys. J. B 92, 221 (2019). https://doi.org/10.1140/epjb/e2019-100165-9

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  • DOI: https://doi.org/10.1140/epjb/e2019-100165-9

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