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A new 5D Hamiltonian conservative hyperchaotic system with four center type equilibrium points, wide range and coexisting hyperchaotic orbits

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Abstract

Based on Euler equation and energy analysis, a new five-dimensional (5D) hyperchaotic system is proposed in this paper. The new system is a conservative system which conforms to the Hamiltonian energy conservation and contains four center type equilibrium points. The conservative and chaotic properties of the system are verified by divergence, phase diagrams, equilibrium points, Lyapunov exponents(LEs), bifurcation diagram and spectral entropy(SE) complexity. In addition, the new system has the characteristics of wide range, which can keep conservative hyperchaotic state and high complexity in wide parameter range and wide initial value range. Besides, with the increase of variable value, the ergodicity and randomness are also enhanced.The multistability phenomenon and transient transition behavior of the new system are analyzed. Finally, the chaotic sequence generated by the new system is verified to have good pseudo-randomness by NIST test, and the physical realizability of the new system is proved by digital signal processor(DSP) hardware platform.

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References

  1. Dong, E., Liu, G., Wang, Z., Chen, Z.: Energy Conservation, Singular Orbits, and FPGA Implementation of Two New Hamiltonian Chaotic Systems. Complexity 2020, 8693157 (2020)

    Google Scholar 

  2. Qi, G., Hu, J., Wang, Z.: Modeling of a Hamiltonian conservative chaotic system and its mechanism routes from periodic to quasiperiodic, chaos and strong chaos. Appl. Math. Model. 78, 350 (2020)

    Article  MathSciNet  Google Scholar 

  3. Vaidyanathan, S., Volos, C.: Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system. Arch. Control Sci. 25(3), 333 (2015)

    Article  MathSciNet  Google Scholar 

  4. Qi, G.: Modelings and mechanism analysis underlying both the 4D Euler equations and Hamiltonian conservative chaotic systems. Nonlinear Dyn. 95(3), 2063 (2018)

    Article  Google Scholar 

  5. Gugapriya, G., Rajagopal, K., Karthikeyan, A., Lakshmi, B.: A family of conservative chaotic systems with cyclic symmetry. Pramana 92(4), 48 (2019)

    Article  Google Scholar 

  6. Chen, M., Wang, C., Wu, H., Xu, Q., Bao, B.: A non-autonomous conservative system and its reconstitution in integral domain. Nonlinear Dyn. 103(1), 643 (2021)

    Article  Google Scholar 

  7. Cang, S., Kang, Z., Wang, Z.: Pseudo-random number generator based on a generalized conservative Sprott-A system. Nonlinear Dyn. 104(1), 827 (2021)

    Article  Google Scholar 

  8. Cang, S., Li, Y., Kang, Z., Wang, Z.: Generating multicluster conservative chaotic flows from a generalized Sprott-A system. Chaos Solitons Fractals 133, 109651 (2020)

    Article  MathSciNet  Google Scholar 

  9. Cang, S., Wu, A., Wang, Z., Chen, Z.: Four-dimensional autonomous dynamical systems with conservative flows: two-case study. Nonlinear Dyn. 89(4), 2495 (2017)

    Article  MathSciNet  Google Scholar 

  10. Chen, G., Ueta, T.: Yet another chaotic attractor. Int. J. Bifurc. Chaos 9(7), 1465 (1999)

    Article  MathSciNet  Google Scholar 

  11. Lu, J., Chen, G., Zhang, S.: Dynamical analysis of a new chaotic attractor. Int. J. Bifurc. Chaos 12(5), 1001 (2002)

    Article  MathSciNet  Google Scholar 

  12. Qi, G., Chen, G., Li, S., Zhang, Y.: Four-wing attractors: from pseudo to real. Int. J. Bifurc. Chaos 16(4), 859 (2006)

    Article  MathSciNet  Google Scholar 

  13. Sprott, J.C.: Some simple chaotic flows. Phys. Rev. E 50(2), R647 (1994)

    Article  MathSciNet  Google Scholar 

  14. Wang, L., Ding, M.: Dynamical analysis and passive control of a new 4D chaotic system with multiple attractors. Mod. Phys. Lett. B 32(22), 1850260 (2018)

    Article  MathSciNet  Google Scholar 

  15. Moysis, L., Volos, C., Stouboulos, I., Goudos, S., Çiçek, S., Pham, V.-T., Mishra, V.K.: A Novel Chaotic System with a Line Equilibrium: Analysis and Its Applications to Secure Communication and Random Bit Generation. Telecom 2020(1), 283 (2020)

    Article  Google Scholar 

  16. Tian, H., Wang, Z., Zhang, P., Chen, M., Wang, Y., Rajagopal, K.: Dynamic Analysis and Robust Control of a Chaotic System with Hidden Attractor. Complexity 2021, 8865522 (2021)

    Google Scholar 

  17. Wang, H., Dong, G.: New dynamics coined in a 4-D quadratic autonomous hyper-chaotic system. Appl. Math. Comput. 346, 272 (2019)

    MathSciNet  MATH  Google Scholar 

  18. Lakshmanan, M., Rajasekar, S.: Nonlinear dynamics: integrability, chaos, and patterns, pp. 285–317. Springer, Berlin (2003)

    Book  Google Scholar 

  19. Dong, E., Yuan, M., Du, S., Chen, Z.: A new class of Hamiltonian conservative chaotic systems with multistability and design of pseudo-random number generator. Appl. Math. Model. 73, 40 (2019)

    Article  MathSciNet  Google Scholar 

  20. Ojoniyi, O.S., Njah, A.N.: A 5D hyperchaotic Sprott B system with coexisting hidden attractors. Chaos Solitons Fractals 87, 172 (2016)

    Article  MathSciNet  Google Scholar 

  21. Li, C., Sprott, J.C., Hu, W., Xu, Y.: Infinite multistability in a self-reproducing chaotic system. Int. J. Bifurc. Chaos 27(10), 1750160 (2017)

    Article  MathSciNet  Google Scholar 

  22. Pham, V.-T., Volos, C., Jafari, S., Kapitaniak, T.: Coexistence of hidden chaotic attractors in a novel no-equilibrium system. Nonlinear Dyn. 87(3), 2001 (2016)

    Article  Google Scholar 

  23. Bao, B., Jiang, T., Xu, Q., Chen, M., Wu, H., Hu, Y.: Coexisting infinitely many attractors in active band-pass filter-based memristive circuit. Nonlinear Dyn. 86(3), 1711 (2016)

    Article  Google Scholar 

  24. Jahanshahi, H., Yousefpour, A., Wei, Z., Alcaraz, R., Bekiros, S.: A financial hyperchaotic system with coexisting attractors: Dynamic investigation, entropy analysis, control and synchronization. Chaos Solitons Fractals 126, 66 (2019)

    Article  MathSciNet  Google Scholar 

  25. Natiq, H., Said, M.R.M., Ariffin, M.R.K., He, S., Rondoni, L., Banerjee, S.: Self-excited and hidden attractors in a novel chaotic system with complicated multistability. Eur. Phys. J Plus 133(12), 557 (2018)

    Article  Google Scholar 

  26. Zhang, S., Zeng, Y., Li, Z., Wang, M., Xiong, L.: Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability. Chaos 28(1), 013113 (2018)

    Article  MathSciNet  Google Scholar 

  27. Abdul Rahim, M. F., Natiq, H., Fataf, N..a.A., Banerjee, S.: Dynamics of a new hyperchaotic system and multistability. Eur. Phys. J Plus 134(10), 499 (2019)

    Article  Google Scholar 

  28. Lai, Q., Xu, G., Pei, H.: Analysis and control of multiple attractors in Sprott B system. Chaos Solitons Fractals 123, 192 (2019)

    Article  MathSciNet  Google Scholar 

  29. Wan, Q., Zhou, Z., Ji, W., Wang, C., Yu, F., Akgul, A.: Dynamic analysis and circuit realization of a novel no-equilibrium 5D memristive hyperchaotic system with hidden extreme multistability. Complexity. 2020, 7106861 (2020)

    Google Scholar 

  30. Jia, H., Shi, W., Wang, L., Qi, G.: Energy analysis of Sprott-A system and generation of a new hamiltonian conservative chaotic system with coexisting hidden attractors. Chaos Solitons Fractals 133, 109635 (2020)

    Article  MathSciNet  Google Scholar 

  31. Singh, J.P., Roy, B.K.: Five new 4-D autonomous conservative chaotic systems with various type of non-hyperbolic and lines of equilibria. Chaos Solitons Fractals 114, 81 (2018)

    Article  MathSciNet  Google Scholar 

  32. Gu, S., Du, B., Wan, Y.: A new four-dimensional non-hamiltonian conservative hyperchaotic system. Int. J. Bifurc. Chaos 30(16), 2050242 (2020)

    Article  MathSciNet  Google Scholar 

  33. Dong, E., Jiao, X., Du, S., Chen, Z., Qi, G.: Modeling, synchronization, and FPGA implementation of hamiltonian conservative hyperchaos. Complexity 2020, 4627597 (2020)

    Google Scholar 

  34. Rajagopal, K., Singh, J.P., Roy, B.K., Karthikeyan, A.: Dissipative and conservative chaotic nature of a new quasi-periodically forced oscillator with megastability. Chin. J Phys. 58, 263 (2019)

    Article  Google Scholar 

  35. Vaidyanathan, S., Sambas, A., Zhang, S., Mohamed, M.A., Mamat, M.: A new hamiltonian chaotic system with coexisting chaotic orbits and its dynamical analysis. Int. J Eng. Technol. 7(4), 2430 (2018)

    Article  Google Scholar 

  36. Gamal, M.M., Mansour, A.: Analysis of chaotic and hyperchaotic conservative complex nonlinear systems. Miskolc Math. Notes. 18(1), 315 (2017)

    Article  MathSciNet  Google Scholar 

  37. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica D 16, 285 (1985)

    Article  MathSciNet  Google Scholar 

  38. Bao, B., Xu, Q., Bao, H.: Memristor circuits and multistability. Science Press, Beijing (2018)

    Google Scholar 

  39. Sun, K., He, S., He, Y., Yin, L.: Complexity analysis of chaotic pseudo-random sequences based on spectral entropy algorithm. Acta Phys. Sin. 62(1), 010501 (2013)

    Article  Google Scholar 

  40. Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., Heckert, A., Dray, J., Vo, S., https://csrc.nist.gov/publications/detail/sp/800-22/rev-1 a/final

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Acknowledgements

This work is partly supported by the National Natural Science Foundation of China (Grant No. 61203004), the Project supported by the Natural Science Foundation of Heilongjiang Province, China(Grant No. F201220) and the project supported by the Joint Guidance Project of the Natural Science Foundation of Heilongjiang Province(Grant No. LH2020 F022)

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Authors and Affiliations

  1. College of Information and Communication Engineering, Harbin Engineering University, Harbin, 150001, People’s Republic of China

    Zefeng Zhang & Lilian Huang

  2. MIIT Key Laboratory of Advanced Marine Communication and Information Technology, Harbin, 150001, People’s Republic of China

    Zefeng Zhang & Lilian Huang

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  1. Zefeng Zhang
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  2. Lilian Huang
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Correspondence to Lilian Huang.

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Zhang, Z., Huang, L. A new 5D Hamiltonian conservative hyperchaotic system with four center type equilibrium points, wide range and coexisting hyperchaotic orbits. Nonlinear Dyn 108, 637–652 (2022). https://doi.org/10.1007/s11071-021-07197-2

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