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Self-excited and hidden attractors in a novel chaotic system with complicated multistability

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Abstract.

In this paper, a new 3D chaotic system with trigonometric function term as a nonlinear controller is proposed. Depending on the nonlinear controller and the value of the parameters, the proposed system exhibits self-excited attractor with an unstable equilibrium, and hidden attractor with no equilibrium or a stable equilibrium. In addition, the unusual and striking dynamic behavior of the coexistence of self-excited chaotic with periodic attractors, two self-excited chaotic attractors with periodic attractor, three periodic attractors, hidden chaotic with point attractors, two hidden chaotic attractors, and four hidden chaotic attractors are explored by selecting appropriate initial values. Consequently, the proposed system has high sensitivity to its initial values and parameters, hence it can be applied in chaos-based cryptographic applications. Thus, the non-periodicity of coexisting attractors of the system is investigated through Lyapunov exponents and Sample Entropy. To demonstrate the performance of the system in real applications, we construct a pseudo-random number generator (PRNG) based on the hidden attractor case. The randomness test results show that the generated PRNG pass all the statistical tests.

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References

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

    Article  ADS  Google Scholar 

  2. O.E. Rössler, Phys. Lett. A 57, 397 (1976)

    Article  ADS  Google Scholar 

  3. J.C. Sprott, Phys. Rev. E 50, R647 (1994)

    Article  ADS  Google Scholar 

  4. G. Chen, T. Ueta, Int. J. Bifurc. Chaos 9, 1465 (1999)

    Article  Google Scholar 

  5. S. Banerjee, S.K. Palit, S. Mukherjee, M. Ariffin, L. Rondoni, Chaos 3, 033105 (2016)

    Article  ADS  Google Scholar 

  6. L. Rondoni, M.R.K. Ariffin, R. Varatharajoo, S. Mukherjee, S.K. Palit, S. Banerjee, Opt. Commun. 387, 257 (2017)

    Article  ADS  Google Scholar 

  7. S. Theesar, Jeeva Sathya, Santo Banerjee, P. Balasubramaniam, Nonlinear Dyn. 70, 1977 (2012)

    Article  Google Scholar 

  8. Papri Saha, Santo Banerjee, A. Roy Chowdhury, Phys. Lett. A 326, 133 (2004)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  10. Alexander N. Pisarchik, Ulrike Feudel, Phys. Rep. 540, 167 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  11. F.T. Arecchi, R. Meucci, G. Puccioni, J. Tredicce, Phys. Rev. Lett. 49, 1217 (1982)

    Article  ADS  Google Scholar 

  12. J.C. Sprott, X. Wang, G. Chen, Int. J. Bifurc. Chaos 23, 1350093 (2013)

    Article  Google Scholar 

  13. C. Li, J.C. Sprott, Int. J. Bifurc. Chaos 24, 1450131 (2014)

    Article  Google Scholar 

  14. J. Kengne, Z.T. Njitacke, H.B. Fotsin, Nonlinear Dyn. 83, 751 (2016)

    Article  Google Scholar 

  15. G. Wang, F. Yuan, G. Chen, Y. Zhang, Chaos 28, 013125 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  16. Guanrong Chen, Chaotification via feedback: the discrete case, in Chaos Control (Springer, Berlin, Heidelberg, 2003) p. 159

  17. Hongjie, Yu, Liu Yanzhu, Phys. Lett. A 314, 292 (2003)

    Article  MathSciNet  Google Scholar 

  18. J.C. Sprott, S. Jafari, A.J.M. Khalaf, T. Kapitaniak, Eur. Phys. J. ST 226, 1979 (2017)

    Article  Google Scholar 

  19. Sajad Jafari, Viet-Thanh Pham, Tomasz Kapitaniak, Int. J. Bifurc. Chaos 26, 1650031 (2016)

    Article  Google Scholar 

  20. Gonzalo Alvarez, Shujun Li, Int. J. Bifurc. Chaos 16, 2129 (2006)

    Article  Google Scholar 

  21. Santo Banerjee, Chaos, Solitons Fractals 42, 745 (2009)

    Article  ADS  Google Scholar 

  22. Santo Banerjee, Sumona Mukhopadhyay, Lamberto Rondoni, Opt. Lasers Eng. 50, 950 (2012)

    Article  Google Scholar 

  23. H. Natiq, N. Al-Saidi, M.R.M. Said, A. Kilicman, Eur. Phys. J. Plus 133, 6 (2018)

    Article  Google Scholar 

  24. H. Natiq, S. Banerjee, S. He, M.R.M. Said, A. Kilicman, Chaos, Solitons Fractals 114, 506 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  25. Zhongyun Hua, Yicong Zhou, Inf. Sci. 339, 237 (2016)

    Article  Google Scholar 

  26. Santo Banerjee, D. Ghosh, A. Roy Chowdhury, Phys. Scr. 78, 015010 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  27. G.C. Layek, An Introduction to Dynamical Systems and Chaos (Springer, New Delhi, 2015)

  28. C.K. Volos, I.M. Kyprianidis, I.N. Stouboulos, Int. J. Multime. Intell. Secur. 1, 320 (2010)

    Google Scholar 

  29. Steven M. Pincus, Proc. Natl. Acad. Sci. 88, 2297 (1991)

    Article  ADS  Google Scholar 

  30. M. Costa, C.K. Peng, A.L. Goldberger, J.M. Hausdorff, Physica A 330, 53 (2003)

    Article  ADS  Google Scholar 

  31. J.S. Richman, J.R. Moorman, Am. J. Physiol.-Heart Circ. Physiol. 278, H2039 (2000)

    Article  Google Scholar 

  32. F. Kaffashi, R. Foglyano, C.G. Wilson, K.A. Loparo, Phys. D 237, 3069 (2008)

    Article  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

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

    Hayder Natiq, M. R. M. Said, M. R. K. Ariffin & Santo Banerjee

  2. Department of Mathematics, Universiti Putra Malaysia, Serdang, Malaysia

    M. R. M. Said

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

    M. R. M. Said, M. R. K. Ariffin, Lamberto Rondoni & Santo Banerjee

  4. Dipartimento di Scienze Matematiche and Graphene@Polito Lab, Politecnico di Torino, Turin, Italy

    Lamberto Rondoni

  5. INFN, Sezione di Torino, Via Pietro Giuria 1, 10125, Torino, Italy

    Lamberto Rondoni

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

    Shaobo He

Authors
  1. Hayder Natiq
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  2. M. R. M. Said
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  3. M. R. K. Ariffin
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  4. Shaobo He
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  5. Lamberto Rondoni
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  6. Santo Banerjee
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Corresponding author

Correspondence to Santo Banerjee.

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Natiq, H., Said, M.R.M., Ariffin, M.R.K. et al. Self-excited and hidden attractors in a novel chaotic system with complicated multistability. Eur. Phys. J. Plus 133, 557 (2018). https://doi.org/10.1140/epjp/i2018-12360-y

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  • DOI: https://doi.org/10.1140/epjp/i2018-12360-y

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