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Complex chaotic attractor via fractal process with parabolic map and triangular map

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Abstract

Chaotic systems and fractal processes have recently been extensively investigated in many fields. In this paper, we propose different systems of fractal process based on Julia’s fractal process, double-scroll chaotic attractor, parabolic map, and triangular map, which can yield different multi-scroll chaotic attractors with different topologies. Furthermore, the results of the numerical simulations are well demonstrated by the micro-controller (MCU) experiments, which reveal the existence of fractal-based multi-scroll chaotic attractors and provide a new idea for the generation of multi-scroll chaotic attractors. From the perspective of engineering applications, the random performance of one of the systems of the fractal process is tested by NIST test suits, and the results confirmed that the systems of the fractal process have excellent randomness and are suitable for image encryption. Therefore, to further verify the randomness of the system of fractal processes, we introduced a new image encryption algorithm with this system of fractal processes as the core. We first replace the pixels in the plain image with the help of an S-box based on chaotic sequences, after which we propose a range-limited pixel diffusion method based on the water wave propagation principle. The simulation results and performance analysis of this algorithm demonstrate that it can effectively hide the information of the plain image, scramble the statistical features such as pixel distribution of the plain image, and at the same time achieve performance improvement compared with other algorithms.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The data that support the findings of this study are available on request from the corresponding author.]

References

  1. L.M. Tam, J.H. Chen, H.K. Chen et al., Chaos Soliton. Fract. 38, 3 (2008)

    Article  Google Scholar 

  2. E.G. Gwinn, R.M. Westervelt, Phys. Rev. Lett. 54, 15 (1985)

    Article  Google Scholar 

  3. J.C. Sprott, Phys. Lett. A 266, 1 (2000)

    Article  Google Scholar 

  4. R.W. Rollins, P. Parmanananda, P. Sherard, Phys. Rev. E 47, 2 (1993)

    Article  Google Scholar 

  5. N. Wang, C. Li, H. Bao et al., IEEE Trans. Circuits I 66, 12 (2019)

    Google Scholar 

  6. W.K.S. Tang, G.Q. Zhong, G. Chen, IEEE Trans. Circuits I 48, 11 (2001)

    Article  Google Scholar 

  7. S. Huan, Q. Li, X.S. Yang, Nonlinear Dyn. 69, 4 (2012)

    Article  Google Scholar 

  8. M.E. Yalcin, J.A.K. Suykens, J. Vandewalle, Int. J. Bifurcat. Chaos 12, 1 (2002)

    Article  Google Scholar 

  9. J. Lu, S. Yu, H. Leung et al., IEEE Trans. Circuits I 53, 1 (2006)

    Article  ADS  Google Scholar 

  10. F. Yuan, G. Wang, X. Wang, Chaos 26, 7 (2016)

    Google Scholar 

  11. C. Wang, X. Liu, H. Xia, Chaos 27, 3 (2017)

    Google Scholar 

  12. X. Xia, Y. Zeng, Z. Li, Pramana 91, 6 (2018)

    Article  ADS  Google Scholar 

  13. P, Liu, R, Xi, P, Ren, et al., Complexity 2018, 1 (2018).

  14. H. Chang, Y. Li, G. Chen, Chaos 30, 4 (2020)

    Google Scholar 

  15. S. Zhang, C. Li, J. Zheng et al., IEEE Trans. Circuits I 68, 12 (2021)

    ADS  Google Scholar 

  16. S. Zhang, J. Zheng, X. Wang et al., Int. J. Bifurcat. Chaos 31, 6 (2021)

    Google Scholar 

  17. K. Bouallegue, Int. J. Bifurcat. Chaos 25, 1 (2015)

    Article  MathSciNet  Google Scholar 

  18. K. Bouallegue, Chaos 25, 7 (2015)

    Article  MathSciNet  Google Scholar 

  19. S. Dai, K. Sun, S. He et al., Entropy 21, 11 (2019)

    Google Scholar 

  20. S.N. Ben, K. Bouallegue, M. Machhout, Nonlinear Dyn. 88, 3 (2017)

    Google Scholar 

  21. D.W. Yan, M.S. Ji’e, L.D. Wang, et al., Nonlinear Dyn. 107, 4 (2022).

  22. X.Y. Du, L.D. Wang, D.W. Yan et al., IEEE T. VLSI. Syst. 29, 12 (2021)

    Article  Google Scholar 

  23. A. Sambas, S. Vaidyanathan, S. Zhang et al., IEEE Access 99, 7 (2019)

    Google Scholar 

  24. B.H. Jasim, K.H. Hassan, K.M. Omran, Int. J. Elect. Comp. Engineer. 11, 3 (2021)

    Google Scholar 

  25. B. Bao, Q. Xu, Y. Xu et al., J. Circuit. Syst. 16, 1 (2011)

    Google Scholar 

  26. M.S. Ji’e, D.W. Yan, L.D. Wang, et al., Int. J. Bifurcat. Chaos 31,11(2021).

  27. W. Xu, N. Cao, J. Circuit. Syst. Comp. 29, 12 (2020)

    Google Scholar 

  28. D.W. Yan, M.S. Ji’e, L.D. Wang, et al., Int. J. Bifurcat. Chaos 32, 07(2022).

  29. Y. Zhang, Sciences 450, 361 (2018)

    Google Scholar 

  30. M.S. Ji’e, D.W. Yan, S.Q. Sun, et al., IEEE Trans. Circuits I 69, 8(2022).

  31. R. Enayatifar, A.H. Abdullah, I.F. Isnin, A. Altameem, M. Lee, Opt. Laser. Eng. 90, 146 (2017)

    Article  Google Scholar 

  32. C. Li, G. Luo, K. Qin, C. Li, Nonlinear Dyn. 87, 127 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

Project supported by the National Key R&D Program of China (Grant No. 2018YFB1306600), the National Natural Science Foundation of China (Grant Nos. 62076207, 62076208, U20A20227), Chongqing Normal University Foundation Project (Grant Nos.22XLB017, 22XLB018).

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Authors and Affiliations

  1. College of Computer and Information Science, Chongqing Normal University, Chongqing, 401331, China

    Dengwei Yan

  2. Key Laboratory of Luminescence Analysis and Molecular Sensing (Southwest University), Ministry of Education, Chongqing, China

    Hang Shi, Jiening Wu, Musha Ji’E, Lidan Wang & Shukai Duan

  3. College of Artificial Intelligence, Southwest University, Chongqing, 400715, China

    Hang Shi, Jiening Wu, Musha Ji’E, Lidan Wang & Shukai Duan

Authors
  1. Dengwei Yan
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  2. Hang Shi
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  3. Jiening Wu
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  4. Musha Ji’E
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  5. Lidan Wang
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  6. Shukai Duan
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All authors contributed equally to this work.

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Correspondence to Dengwei Yan or Lidan Wang.

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Yan, D., Shi, H., Wu, J. et al. Complex chaotic attractor via fractal process with parabolic map and triangular map. Eur. Phys. J. Plus 138, 343 (2023). https://doi.org/10.1140/epjp/s13360-023-03904-7

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