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A novel 2D non-autonomous discrete memristor-based hyperchaotic map and its hardware implementation

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Abstract

Many achievements have been made in the study of bursting oscillations of continuous-time chaotic systems and memristor coupled chaotic maps. However, the study of bursting oscillations in coupled maps of discrete memristors (DMs) has not received sufficient attention. Therefore, in this paper, a new non-autonomous discrete memristor (NDM) is coupled with a sine map, and a novel 2D NDM-based hyperchaotic (NDMH) map with a line of fixed points is established. The NDMH map exhibits complex dynamical behavior such as bursting oscillations, amplitude control, attractor rotation, and chaotic sequence displacement. Finally, the numerical results are verified by hardware experiments.

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The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

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

    Article  Google Scholar 

  2. Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 453(7191), 80–83 (2008)

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Buscarino, A., Fortuna, L., Frasca, M., Valentina Gambuzza, L.: A chaotic circuit based on Hewlett–Packard memristor. Chaos 22(2), 023136 (2012)

    Article  MathSciNet  Google Scholar 

  5. Lai, Q., Wan, Z., Kuate, P.D.K., Fotsin, H.: Coexisting attractors, circuit implementation and synchronization control of a new chaotic system evolved from the simplest memristor chaotic circuit. Commun. Nonlinear Sci. 89, 105341 (2020)

    Article  MathSciNet  Google Scholar 

  6. Guo, Z.H., Li, Z.J., Wang, M.J., Ma, M.L.: Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh–Nagumo neurons with two time delays. Chin. Phys. B 32(3), 038701 (2023)

    Article  Google Scholar 

  7. Li, C., Yang, Y., Yang, X., Zi, X., Xiao, F.: A tristable locally active memristor and its application in Hopfield neural network. Nonlinear Dyn. 108, 1697–1717 (2022)

    Article  Google Scholar 

  8. Lin, H., Wang, C., Sun, Y., Yao, W.: Firing multistability in a locally active memristive neuron model. Nonlinear Dyn. 100, 3667–3683 (2020)

    Article  Google Scholar 

  9. Lin, H., Wang, C., Deng, Q., Xu, C., Deng, Z., Zhou, C.: Review on chaotic dynamics of memristive neuron and neural network. Nonlinear Dyn. 106, 959–973 (2021)

    Article  Google Scholar 

  10. Peng, C., Li, Z., Wang, M., Ma, M.: Dynamics in a memristor-coupled heterogeneous neuron network under electromagnetic radiation. Nonlinear Dyn. 111, 16527–16543 (2023)

    Article  Google Scholar 

  11. Li, Y., Jiang, F.: Firing activities in a second-order memristor-based Hindmarsh–Rose neuron. Chin. J. Phys. (2024)

  12. Ma, X., Mou, J., Xiong, L., Banerjee, S., Cao, Y., Wang, J.: A novel chaotic circuit with coexistence of multiple attractors and state transition based on two memristors. Chaos Solitons Fractals 152, 111363 (2021)

    Article  MathSciNet  Google Scholar 

  13. Lai, Q., Wan, Z., Kuate, P.D.K., Fotsin, H.: Coexisting attractors, circuit implementation and synchronization control of a new chaotic system evolved from the simplest memristor chaotic circuit. Commun. Nonlinear Sci. Num. Simul. 89, 105341 (2020)

    Article  MathSciNet  Google Scholar 

  14. Wang, N., Zhang, G., Bao, H.: Initial condition-dependent dynamics and transient period in memristor-based hypo-genetic jerk system with four line equilibria. Nonlinear Dyn. 97, 1477–1494 (2019)

    Article  Google Scholar 

  15. Chen, M., Yu, J., Bao, B.C.: Finding hidden attractors in improved memristor-based Chua’s circuit. Electron. Lett. 51(6), 462–464 (2015)

    Article  Google Scholar 

  16. Zhang, S., Li, C., Zheng, J., Wang, X., Zeng, Z., Chen, G.: Generating any number of diversified hidden attractors via memristor coupling. IEEE Trans. Circ. Syst. I Reg. Pap. 68(12), 4945–4956 (2021)

    Article  Google Scholar 

  17. Chen, M., Li, M., Yu, Q., Bao, B., Xu, Q., Wang, J.: Dynamics of self-excited attractors and hidden attractors in generalized memristor-based Chua’s circuit. Nonlinear Dyn. 81, 215–226 (2015)

    Article  MathSciNet  Google Scholar 

  18. Wang, M.J., Gu, L.F.: Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic Jerk system with multiple cubic nonlinearity. Chin. Phys. B 33, 020504 (2024)

    Article  Google Scholar 

  19. Guo, M., Yang, W., Xue, Y., Gao, Z., Yuan, F., Dou, G., Li, Y.: Multistability in a physical memristor-based modified Chua’s circuit. Chaos 29(4), 043114 (2019)

    Article  MathSciNet  Google Scholar 

  20. Yuan, F., Wang, G., Wang, X.: Extreme multistability in a memristor-based multi-scroll hyper-chaotic system. Chaos 26(7), 073107 (2016)

    Article  MathSciNet  Google Scholar 

  21. Wu, H.G., Ye, Y., Bao, B.C., Chen, M., Xu, Q.: Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system. Chaos Solitons Fractals 121, 178–185 (2019)

    Article  MathSciNet  Google Scholar 

  22. Jia, S.H., Li, Y.X., Shi, Q.Y., Huang, X.: Design and FPGA implementation of a memristor-based multi-scroll hyperchaotic system. Chin. Phys. B 31(7), 070505 (2022)

    Article  Google Scholar 

  23. Wang, J., Cao, Y., Mou, J., Liu, X.: Double memristors series hyperchaotic system with attractive coexistence and its circuit implementation. Eur. Phys. J. Spec. Top. 230(21), 3901–3912 (2021)

    Article  Google Scholar 

  24. Kong, X., Yu, F., Yao, W., Xu, C., Zhang, J., Cai, S., Wang, C.: A class of 2n+ 1 dimensional simplest Hamiltonian conservative chaotic systems and fast image encryption schemes. Appl. Math. Model. 125, 350–374 (2024)

    Article  MathSciNet  Google Scholar 

  25. He, S., Sun, K., Peng, Y., Wang, L.: Modeling of discrete fracmemristor and its application. AIP Adv. 10(1), 015332 (2020)

    Article  Google Scholar 

  26. Li, H., Li, C., Du, J.: Discretized locally active memristor and application in logarithmic map. Nonlinear Dyn. 111(3), 2895–2915 (2023)

    Article  Google Scholar 

  27. Wang, M., An, M., Zhang, X., Iu, H.H.C.: Feedback control-based parallel memristor-coupled sine map and its hardware implementation. IEEE Trans. Circuits Syst. II Exp. Briefs 70(11), 4251–4255 (2023)

    Google Scholar 

  28. He, S., Liu, J., Wang, H., Sun, K.: A discrete memristive neural network and its application for character recognition. Neurocomputing 523, 1–9 (2023)

  29. Peng, Y., Liu, J., He, S., Sun, K.: Discrete fracmemristor-based chaotic map by Grunwald–Letnikov difference and its circuit implementation. Chaos Solitons Fractals 171, 113429 (2023)

    Article  MathSciNet  Google Scholar 

  30. Abobda, L.T., Woafo, P.: Subharmonic and bursting oscillations of a ferromagnetic mass fixed on a spring and subjected to an AC electromagnet. Commun. Nonlinear Sci. Numer. Simul. 17, 3082–3091 (2012)

    Article  MathSciNet  Google Scholar 

  31. Courbage, M., Maslennikov, O.V., Nekorkin, V.I.: Synchronization in time-discrete model of two electrically coupled spike-bursting neurons. Chaos Solitons Fractals 45, 645–659 (2012)

    Article  Google Scholar 

  32. Han, X., Jiang, B., Bi, Q.: Symmetric bursting of focus–focus type in the controlled Lorenz system with two time scales. Phys. Lett. A 373, 3643–3649 (2009)

    Article  Google Scholar 

  33. Bi, Q., Li, S., Kurths, J., Zhang, Z.: The mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures. Nonlinear Dyn. 85, 993–1005 (2016)

    Article  MathSciNet  Google Scholar 

  34. Wang, M., Li, J., Yu, S.S., Zhang, X., Li, Z., Iu, H.H.: A novel 3D non-autonomous system with parametrically excited abundant dynamics and bursting oscillations. Chaos 30(4), 043125 (2020)

    Article  MathSciNet  Google Scholar 

  35. Wang, H., Wang, Q., Lu, Q.: Bursting oscillations, bifurcation and synchronization in neuronal systems. Chaos Solitons Fractals 44(8), 667–675 (2011)

    Article  Google Scholar 

  36. Wen, Z., Li, Z., Li, X.: Bursting oscillations and bifurcation mechanism in memristor-based Shimizu-Morioka system with two time scales. Chaos Solitons Fractals 128, 58–70 (2019)

    Article  MathSciNet  Google Scholar 

  37. Deng, Y., Li, Y.: Symmetrical Hopf-induced bursting and hyperchaos control in memristor-based circuit. Chaos 31(4), 043103 (2021)

    Article  MathSciNet  Google Scholar 

  38. Chang, H., Li, Y., Chen, G.: A novel memristor-based dynamical system with multi-wing attractors and symmetric periodic bursting. Chaos 30(4), 146–153 (2020)

    Article  MathSciNet  Google Scholar 

  39. Jiang, Y.D., Zhang, W., Zhang, Y.F., Bi, Q.S.: Bursting oscillations in coupling Mathieu–van der Pol oscillator under parametric excitation. Chaos Solitons Fractals 178, 114279 (2024)

    Article  MathSciNet  Google Scholar 

  40. Vijay, S.D., Thamilmaran, K., Ahamed, A.I.: Superextreme spiking oscillations and multistability in a memristor-based Hindmarsh–Rose neuron model. Nonlinear Dyn. 111, 789–799 (2023)

    Article  Google Scholar 

  41. Bashkirtseva, I., Ryashko, L.: Transformations of spike and burst oscillations in the stochastic Rulkov model. Chaos Solitons Fractals 170, 113414 (2023)

    Article  MathSciNet  Google Scholar 

  42. Li, K., Bao, B., Ma, J., Chen, M., Bao, H.: Synchronization transitions in a discrete memristor-coupled bi-neuron model. Chaos Solitons Fractals 165, 112861 (2022)

    Article  Google Scholar 

  43. Sprott, J.C.: A proposed standard for the publication of new chaotic systems. Int. J. Bifurc. Chaos 21, 2391–2394 (2011)

    Article  Google Scholar 

  44. Bao, H., Hua, Z., Li, H., Chen, M., Bao, B.: Discrete memristor hyperchaotic maps. IEEE Trans. Circ. Syst. I Reg. Pap. 68(11), 4534–4544 (2021)

  45. Deng, Y., Li, Y.: Bifurcation and bursting oscillations in 2D non-autonomous discrete memristor-based hyperchaotic map. Chaos Solitons Fractals 150, 111064 (2021)

  46. Njitacke, Z.T., Tsafack, N., Ramakrishnan, B., Rajagopal, K., Kengne, J., Awrejcewicz, J.: Complex dynamics from heterogeneous coupling and electromagnetic effect on two neurons: application in images encryption. Chaos Solitons Fractals 153, 111577 (2021)

    Article  MathSciNet  Google Scholar 

  47. Njitacke, Z.T., Koumetio, B.N., Ramakrishnan, B., Leutcho, G.D., Fozin, T.F., Tsafack, N., Rajagopal, K., Kengne, J.: Hamiltonian energy and coexistence of hidden firing patterns from bidirectional coupling between two different neurons. Cogn. Neurodyn. 16, 899–916 (2022)

    Article  Google Scholar 

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Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62071411 and 62171401) and the Research Foundation of Education Department of Hunan Province, China (Grant No. 20B567).

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Authors and Affiliations

  1. School of Automation and Electronic Information, Xiangtan University, North Second Ring Road, Xiangtan, 411105, Hunan, China

    Mengjiao Wang, Jie Ding & Zhijun Li

  2. School of Electrical, Electronic and Computer Engineering, University of Western Australia, 35 Stirling Hwy, Perth, WA, 6009, Australia

    Herbert Ho-Ching Iu

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  1. Mengjiao Wang
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Correspondence to Mengjiao Wang.

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Wang, M., Ding, J., Li, Z. et al. A novel 2D non-autonomous discrete memristor-based hyperchaotic map and its hardware implementation. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09669-7

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