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Dynamical properties and complexity in fractional-order diffusionless Lorenz system

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Abstract.

In this paper, dynamics and complexity of the fractional-order diffusionless Lorenz system which is solved by the developed discrete Adomian decomposition method are investigated numerically. Dynamical properties of the fractional-order diffusionless Lorenz system with the control parameter and derivative order varying is analyzed by using bifurcation diagrams, and period-doubling route to chaos in different cases is observed. The complexity of the system is investigated by means of Lyapunov characteristic exponents, multi-scale spectral entropy algorithm and multiscale Renyi permutation entropy algorithm. It can be observed that the three methods illustrate consistent results and the system has rich complex dynamics. Interestingly, complexity decreases with the increase of derivative order. It shows that the fractional-order diffusionless Lorenz system is a good model for real applications such as information encryption and secure communication.

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References

  1. M. Ichise, Y. Nagayanagi, T. Kojima, J. Electroanal. Chem. 2, 253 (1971)

    Article  Google Scholar 

  2. M.S. Tavazoei, M. Haeri, Automatica 45, 1886 (2009)

    Article  MathSciNet  Google Scholar 

  3. H.Y. Jia, Q. Tao, Z.Q. Chen, Syst. Sci. Control Eng. 2, 745 (2014)

    Article  Google Scholar 

  4. K.H. Sun, X. Wang, J.C. Sprott, Int. J. Bifurcat. Chaos 20, 1209 (2010)

    Article  MathSciNet  Google Scholar 

  5. C. Li, G.R. Chen, Chaos Solitons Fractals 22, 549 (2004)

    Article  ADS  Google Scholar 

  6. R.L. Tian, Q.L. Wu, Y.P. Xiong, Eur. Phys. J. Plus 129, 85 (2014)

    Article  ADS  Google Scholar 

  7. X.R. Lin, S.b. Zhou, H. Li, Int. J. Bifurcat. Chaos 26, 1650046 (2016)

    Article  Google Scholar 

  8. C. Li, G.R. Chen, Physica A 341, 55 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  9. S.T. Kingni, S. Jafari, H. Simo, Eur. Phys. J. Plus 129, 76 (2014)

    Article  Google Scholar 

  10. A.Y.T. Leung, X.F. Li, Y.D. Chu, Nonlinear Dyn. 82, 185 (2015)

    Article  MathSciNet  Google Scholar 

  11. Z. Wang, X. Huang, N. Li, Chin. Phys. B 21, 107 (2012)

    Google Scholar 

  12. B.A. Kiani, K. Fallahi, N. Pariz, Commun. Nonlinear Sci. Numer. Simulat. 14, 863 (2009)

    Article  ADS  Google Scholar 

  13. J.C. Sprott, Phys. Rev. E 50, 647 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  14. G.V.D. Schrier, L.R.M. Maas, Physica D 141, 19 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  15. J.C. Sprott, Chaos 17, 033124 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  16. A. Dwivedi, A.K. Mittal, S. Dwivedi, IET Commun. 6, 2016 (2012)

    Article  MathSciNet  Google Scholar 

  17. Y. Xu, R.C. Gu, H.Q. Zhang, Int. J. Bifurcat. Chaos 22, 427 (2012)

    Google Scholar 

  18. K.H. Sun, J.C. Sprott, Electr. J. Theor. Phys. 6, 123 (2009)

    Google Scholar 

  19. K. Diethelm, Electr. Trans. Numer. Anal. 5, 1 (1997)

    MathSciNet  Google Scholar 

  20. R. Caponetto, S. Fazzino, Int. J. Bifurcat. Chaos 23, 1350050 (2013)

    Article  MathSciNet  Google Scholar 

  21. S.B. He, K.H. Sun, H.H. Wang, Entropy 17, 8299 (2015)

    Article  ADS  Google Scholar 

  22. R. Caponetto, S. Fazzino, Commun. Nonlinear Sci. Numer. Simulat. 18, 22 (2013)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  24. B. Christoph, P. Bernd, Phys. Rev. Lett. 88, 174102 (2002)

    Article  Google Scholar 

  25. J. Lee, L. Mcgough, B.R. Safdi, Phys. Rev. D 89, 115 (2014)

    Google Scholar 

  26. W.T. Chen, J.W. Zhuang, Z. Wang, Med. Eng. Phys. 31, 61 (2009)

    Article  Google Scholar 

  27. K.H. Sun, S.B. He, Y. He, Acta Phys. Sinica 62, 010501 (2013)

    Google Scholar 

  28. Z.J. Cai, J. Sun, Int. J. Bifurcat. Chaos 19, 977 (2011)

    Article  MathSciNet  Google Scholar 

  29. M. Costa, A.L. Goldberger, C.K. Peng, Phys. Rev. Lett. 89, 705 (2002)

    Article  Google Scholar 

  30. K. Cho, T. Miyano, Nonlinear Theor. Appl. 7, 21 (2016)

    ADS  Google Scholar 

  31. S. Mukherjee, S.K. Palit, S. Banerjee, Physica A 439, 93 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  32. N.S. Liu, Commun. Nonlinear Sci. Numer. Simulat. 16, 761 (2011)

    Article  ADS  Google Scholar 

  33. R. Gorenflo, F. Mainardi, Fractal and Fractional Calculus in Continuum Mechanics (Springer-Verlag, Wien, 1997)

  34. F. Hubertus, F.E. Udwadia, W. Proskurowski, Physica D 101, 1 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  35. S. Lv, M. Zhao, Chaos Solitons Fractals 37, 1469 (2008)

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Physics and Electronics, Central South University, 410083, Changsha, China

    Shaobo He & Kehui Sun

  2. Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia

    Santo Banerjee

  3. Malaysia-Italy Centre of Excellence for Mathematical Science, Universiti Putra Malaysia, Serdang, Malaysia

    Santo Banerjee

Authors
  1. Shaobo He
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  2. Kehui Sun
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  3. Santo Banerjee
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Correspondence to Kehui Sun.

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He, S., Sun, K. & Banerjee, S. Dynamical properties and complexity in fractional-order diffusionless Lorenz system. Eur. Phys. J. Plus 131, 254 (2016). https://doi.org/10.1140/epjp/i2016-16254-8

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  • DOI: https://doi.org/10.1140/epjp/i2016-16254-8

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