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Double memristors series hyperchaotic system with attractive coexistence and its circuit implementation

Abstract

In this paper, the sine function memristor and the cosine function memristor are connected in series, and the constructed series memristor is numerically analyzed through its volt-ampere characteristics, and then the new memristor was introduced into the Rossler system to construct a hyperchaotic system with dual memory elements. The coexistence attractor and fractal phenomena in the system are analyzed, and the fractal dimension of the system is calculated on the basis of fractal theory. In addition, analog circuits corresponding to the system are designed and simulated based on circuit theory. DSP is used for digital circuit experiments to explore the application of this system in practice.

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Data availability statement

This manuscript has associated data in a data repository [Authors’ comment: All data included in this manuscript are available upon request by contacting with the corresponding author.]

References

  1. 1.

    S. Haykin, S. Puthusserypady, Chaotic dynamics of sea clutter. Chaos (Woodbury, NY) 7, 777–802 (1998)

    MATH  Google Scholar 

  2. 2.

    Juan Barajas-Ramìrez, Arturo Franco-López, Hugo Gonzalez-Hernandez, Generating Shilnikov chaos in 3D piecewise linear systems. Appl. Math. Comput. 395, 125877 (2021). https://doi.org/10.1016/j.amc.2020.125877

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    P. Gauthier, Chaos and quadri-dimensional data assimilation: a study based on the Lorenz model. Tellus A 44(1), 2–17 (1992)

    ADS  Google Scholar 

  4. 4.

    Y.-Q. Zhang, X.-Y. Wang, J. Liu, Z.-L. Chi, An image encryption scheme based on the MLNCML system using DNA sequences. Opt. Lasers Eng. 82, 95–103 (2016)

    Google Scholar 

  5. 5.

    R.M. May, Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos (in eng). Science 186(4164), 645–7 (1974)

    ADS  Google Scholar 

  6. 6.

    J.N. Weiss, A. Garfinkel, M.L. Spano, W.L. Ditto, Chaos and chaos control in biology (in eng). J. Clin. Investig. 93(4), 1355–60 (1994)

    Google Scholar 

  7. 7.

    T.D. Rogers, Chaos in systems in population biology, in Progress in Theoretical Biology, vol. 6, pp. 90–146 (1981)

  8. 8.

    M.J. Feigenbaum, Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. 19(1), 25–52 (1978)

    ADS  MathSciNet  MATH  Google Scholar 

  9. 9.

    T. Liu, S. Banerjee, H. Yan, J. Mou, Dynamical analysis of the improper fractional-order 2D-SCLMM and its DSP implementation. Eur. Phys. J. Plus 136(5), 506 (2021)

    Google Scholar 

  10. 10.

    J. L. Mccauley, Chaos, Dynamics, and Fractals: an Algorithmic Approach to Determinstic Chaos[M] (Cambridge University Press, 1993)

  11. 11.

    F. Zhang, L. Xu, J. Wang, The dynamic and thermodynamic origin of dissipative chaos: chemical Lorenz system. Phys. Chem. Chem. Phys. 22, 27896–902 (2020)

    Google Scholar 

  12. 12.

    A. Datta, A. Mukherjee, A.K. Ghosh, Simulation and analysis of a chaos-masking communication scheme based on electronic simulator for electro-optic modulator with noise. SN Comput. Sci. 2(4), 240 (2021)

    Google Scholar 

  13. 13.

    A. Chithra, T.F. Fozin, K. Srinivasan, E.R.M. Kengne, A.T. Kouanou, I.R. Mohamed, Complex dynamics in a memristive diode bridge-based MLC circuit: coexisting attractors and double-transient chaos. Int. J. Bifurc. Chaos 31(03), 2150049 (2021)

    MathSciNet  MATH  Google Scholar 

  14. 14.

    H. Zhang, X.-F. Li, A.Y.T. Leung, A calculation method on bifurcation and state parameter sensitivity analysis of piecewise mechanical systems. Int. J. Bifurc. Chaos 30(11), 2030033 (2020)

    MathSciNet  MATH  Google Scholar 

  15. 15.

    P. Sharma, T. Jain, V. Sethi, V. Dudeja, Symphony in chaos: immune orchestra during pancreatic cancer progression. EBioMedicine 56, 102787 (2020)

    Google Scholar 

  16. 16.

    D.V. Guseinov, I.V. Matyushkin, N.V. Chernyaev, A.N. Mikhaylov, Y.V. Pershin, Capacitive effects can make memristors chaotic. Chaos, Solitons Fractals 144, 110699 (2021)

    MathSciNet  Google Scholar 

  17. 17.

    X. Li, Z. Feng, Q. Zhang, X. Wang, G. Xu, Scaling of attractors of a multiscroll memristive chaotic system and its generalized synchronization with sliding mode control. Int. J. Bifurc. Chaos 31(01), 2150007 (2021)

    MathSciNet  MATH  Google Scholar 

  18. 18.

    C. Du, L. Liu, Z. Zhang, S. Yu, A coupling method of double memristors and analysis of extreme transient behavior. Nonlinear Dyn. 104(1), 765–787 (2021)

    Google Scholar 

  19. 19.

    A. Ascoli, S. Slesazeck, H. Mähne, R. Tetzlaff, T. Mikolajick, Nonlinear dynamics of a locally-active memristor. IEEE Trans. Circuits Syst. I Regul. Pap. 62(4), 1165–1174 (2015)

  20. 20.

    L. Chua, Memristor—the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971)

    Google Scholar 

  21. 21.

    Y.N. Joglekar, S.J. Wolf, The elusive memristor: properties of basic electrical circuits. Eur. J. Phys. 30(4), 661–675 (2009)

    MATH  Google Scholar 

  22. 22.

    L.O. Chua, Y. Tao, Z. Guo-Qun, W. Chai Wah, Synchronization of Chua’s circuits with time-varying channels and parameters. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 43(10), 862–868 (1996)

  23. 23.

    L. Chua, Resistance switching memories are memristors. Appl. Phys. A 102(4), 765–783 (2011)

    ADS  MATH  Google Scholar 

  24. 24.

    X. Ma, J. Mou, J. Liu, C. Ma, F. Yang, X. Zhao, A novel simple chaotic circuit based on memristor-memcapacitor. Nonlinear Dyn. 100(3), 2859–2876 (2020)

    Google Scholar 

  25. 25.

    Z. Qu et al., A novel WOx-based memristor with a Ti nano-island array. Electrochim. Acta 377, 138123 (2021)

    Google Scholar 

  26. 26.

    Y. Shen, G. Wang, History erase effect of real memristors. Electronics 10, 303 (2021)

    Google Scholar 

  27. 27.

    M. Itoh, L. Chua, Memristor cellular automata and memristor discrete-time cellular neural networks, in Memristor Networks. ed. by A. Adamatzky, L. Chua (Springer International Publishing, Cham, 2014), pp. 649–713

    MATH  Google Scholar 

  28. 28.

    S. Kim, C. Du, P. Sheridan, W. Ma, S. Choi, W.D. Lu, Experimental demonstration of a second-order memristor and its ability to biorealistically implement synaptic plasticity. Nano Lett. 15(3), 2203–2211 (2015)

    ADS  Google Scholar 

  29. 29.

    H. Abdalla, M.D. Pickett, SPICE modeling of memristors. In: IEEE International Symposium of Circuits and Systems (ISCAS), 2011, pp. 1832–1835 (2011)

  30. 30.

    S. Benderli, T.A. Wey, On SPICE macromodelling of TiO2 memristors. Electron. Lett. IEE 45(7), 377–378 (2009)

    ADS  Google Scholar 

  31. 31.

    Y.-Q. Zhang, X.-Y. Wang, L.-Y. Liu, Y. He, J. Liu, Spatiotemporal chaos of fractional order logistic equation in nonlinear coupled lattices. Commun. Nonlinear Sci. Num. Simul. 52, 52–61 (2017)

    MathSciNet  MATH  Google Scholar 

  32. 32.

    L. Xiong, X. Zhang, Y. Chen, Experimental verification of volt-ampere characteristic curve for a memristor-based chaotic circuit. Circuit World 46(1), 13–24 (2020)

    Google Scholar 

  33. 33.

    Y. Shen, G. Wang, Y. Liang, S. Yu, H.H. Iu, Parasitic memcapacitor effects on HP TiO2 memristor dynamics. IEEE Access 7, 59825–59831 (2019)

    Google Scholar 

  34. 34.

    X. Wang, S. Wang, Y. Zhang, C. Luo, A one-time pad color image cryptosystem based on SHA-3 and multiple chaotic systems. Opt. Lasers Eng. 103, 1–8 (2018)

    Google Scholar 

  35. 35.

    A. Buscarino, L. Fortuna, M. Frasca, L.V. Gambuzza, G. Sciuto, Memristive chaotic circuits based on cellular nonlinear networks. Int. J. Bifurc. Chaos 22(03), 1250070 (2012)

    Google Scholar 

  36. 36.

    A.I. Ahamed, K. Srinivasan, K. Murali, M. Lakshmanan, Observation of chaotic beats in a driven memristive Chua’s circuit. Int. J. Bifurc. Chaos 21(03), 737–757 (2011)

    MATH  Google Scholar 

  37. 37.

    L.O. Chua, C.W. Wu, A. Huang, Z. Guo-Qun, A universal circuit for studying and generating chaos. I. Routes to chaos. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 40(10), 732–744 (1993)

  38. 38.

    T. Matsumoto, Chaos in electronic circuits. Proc. IEEE 75(8), 1033–1057 (1987)

    ADS  Google Scholar 

  39. 39.

    H. Wu, H. Zhu, G. Ye, Public key image encryption algorithm based on pixel information and random number insertion. Phys. Scr. 96(10), 105202 (2021)

    ADS  Google Scholar 

  40. 40.

    Y. Liu, Z. You, Multi-stability and almost periodic solutions of a class of recurrent neural networks. Chaos Solitons Fractals 33(2), 554–563 (2007)

    ADS  MathSciNet  MATH  Google Scholar 

  41. 41.

    M. Chen, J. Yu, B.-C. Bao, Hidden dynamics and multi-stability in an improved third-order Chua’s circuit. J. Eng. 2015(10), 322–324 (2015). https://doi.org/10.1049/joe.2015.0149

    Article  Google Scholar 

  42. 42.

    A.O. Adelakun, Resonance oscillation and transition to chaos in \(\phi ^8\)-Duffing–Van der Pol oscillator. Int. J. Appl. Comput. Math. 7(3), 82 (2021)

  43. 43.

    Y.-Q. Zhang, X.-Y. Wang, Spatiotemporal chaos in mixed linear-nonlinear coupled logistic map lattice. Phys. A Stat. Mech. Appl. 402, 104–118 (2014)

    MathSciNet  MATH  Google Scholar 

  44. 44.

    L. Zhang, H. Jiang, Y. Liu, Z. Wei, Q. Bi, Controlling hidden dynamics and multistability of a class of two-dimensional maps via linear augmentation. Int. J. Bifurc. Chaos 31(03), 2150047 (2021)

    MathSciNet  MATH  Google Scholar 

  45. 45.

    F. Yang, J. Mou, C. Ma, Y. Cao, Dynamic analysis of an improper fractional-order laser chaotic system and its image encryption application. Opt. Lasers Eng. 129, 106031 (2020)

    Google Scholar 

  46. 46.

    C. Ma, J. Mou, P. Li, T. Liu, Dynamic analysis of a new two-dimensional map in three forms: integer-order, fractional-order and improper fractional-order. Eur. Phys. J. Spec. Top. (2021)

  47. 47.

    G. Dou et al., Coexisting multi-dynamics of a physical SBT memristor-based chaotic circuit. Int. J. Bifurc. Chaos 30(11), 2030043 (2020)

    MathSciNet  MATH  Google Scholar 

  48. 48.

    T. Yang, Multistability and hidden attractors in a three-dimensional chaotic system. Int. J. Bifurc. Chaos 30(06), 2050087 (2020)

    MathSciNet  MATH  Google Scholar 

  49. 49.

    Y. Wang, P. Shang, Complexity analysis of time series based on generalized fractional order refined composite multiscale dispersion entropy. Int. J. Bifurc. Chaos 30(14), 2050211 (2020)

    MathSciNet  MATH  Google Scholar 

  50. 50.

    J.P. Eckmann, D. Ruelle, Addendum: ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57(4), 1115–1115 (1985)

    ADS  MathSciNet  MATH  Google Scholar 

  51. 51.

    T. Liu, H. Yan, S. Banerjee, J. Mou, A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation. Chaos Solitons Fractals 145, 110791 (2021)

  52. 52.

    X. Shang, P. Ma, M. Yang, T. Chao, An efficient polynomial chaos-enhanced radial basis function approach for reliability-based design optimization. Struct. Multidiscip. Optim. 63(2), 789–805 (2021)

    MathSciNet  Google Scholar 

  53. 53.

    X. Li, J. Mou, L. Xiong, Z. Wang, J. Xu, Fractional-order double-ring erbium-doped fiber laser chaotic system and its application on image encryption. Opt. Laser Technol. 140, 107074 (2021)

    Google Scholar 

  54. 54.

    C. Xiu, R. Zhou, S. Zhao, G. Xu, Memristive hyperchaos secure communication based on sliding mode control. Nonlinear Dyn. 104(1), 789–805 (2021)

    Google Scholar 

  55. 55.

    J.H. Park, Adaptive synchronization of Rossler system with uncertain parameters. Chaos Solitons Fractals 25(2), 333–338 (2005)

    ADS  MathSciNet  MATH  Google Scholar 

  56. 56.

    C. Li, X. Liao, Lag synchronization of Rossler system and Chua circuit via a scalar signal. Phys. Lett. A 329(4), 301–308 (2004)

    ADS  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 62061014); Natural Science Foundation of Liaoning (2020-MS-274); The Basic Scientific Research Projects of Colleges and Universities of Liaoning (Grant No. J202148).

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Contributions

JW designed and carried out experiments, data analyzed and wrote manuscript. YC and JM made the theoretical guidance for this paper. XL carried out experiment. JM improved the algorithm. All authors reviewed the manuscript.

Corresponding authors

Correspondence to Yinghong Cao or Jun Mou.

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Wang, J., Cao, Y., Mou, J. et al. Double memristors series hyperchaotic system with attractive coexistence and its circuit implementation. Eur. Phys. J. Spec. Top. (2021). https://doi.org/10.1140/epjs/s11734-021-00330-7

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