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A memristor-coupled heterogeneous discrete neural networks with infinite multi-structure hyperchaotic attractors

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Abstract

In this paper, a discrete memristor-coupled heterogeneous neural network (MCHNN) by coupling KTz neuron and tabu learning neurons with a locally active discrete memristor is constructed. Firstly, rationale of the proposed discrete MCHNN is presented. Then, taking the memristor initial state and coupling weight as variables, the abundant dynamical behaviors of the coupled neuron network are systematically analyzed, as well as the multi-stability of the discrete bi-neuron network are proved. Particularly, the six different firing cases and three types infinite multi-structure hyperchaotic attractors are discussed. Finally, a microcontroller-based hardware experiment was also conducted, in order to further verify the correctness of the numerical simulation. This study provides a theoretical basis for the implementation of MCHNN in human brain dynamics.

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Data availability statement

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

References

  1. B. Bao, A. Hu, H. Bao et al., Three-dimensional memristive Hindmarsh–Rose neuron model with hidden coexisting asymmetric behaviors. Complexity 2018, 1–11 (2018)

    ADS  Google Scholar 

  2. M. Ma, Y. Lu, Z. Li et al., Multistability and phase synchronization of Rulkov neurons coupled with a locally active discrete memristor. Fractal Fractional. 7(1), 82 (2023)

    Article  Google Scholar 

  3. M. Ma, K. Xiong, Z. Li et al., Dynamic Behavior analysis and synchronization of memristor-coupled heterogeneous discrete neural networks. Mathematics. 11(2), 375 (2023)

    Article  Google Scholar 

  4. B. Bao, Q. Yang, D. Zhu et al., Initial-induced coexisting and synchronous firing activities in memristor synapse-coupled Morris–Lecar bi-neuron network. Nonlinear Dyn. 99(3), 2339–2354 (2019)

    Article  Google Scholar 

  5. G.S. Bortolotto, R.V. Stenzinger, M.H. Tragtenberg, Electromagnetic induction on a map-based action potential model. Nonlinear Dyn. 95(1), 433–444 (2018)

    Article  Google Scholar 

  6. Chialvo, D.R., Girardi Schappo, M., Bortolotto, G.S., et al.: Phase diagrams and dynamics of a computationally efficient map-based neuron model. Plos One. 12(3) (2017)

  7. M. Courbage, V. Nekorkin, L. Vdovin, Chaotic oscillations in a map-based model of neural activity. Chaos: Interdiscip. J. Nonlinear Sci. 17(4), 043109 (2007)

  8. M. Courbage, V.I. Nekorkin, Map based models in neurodynamics. Int. J. Bifurc. Chaos. 20(06), 1631–1651 (2010)

    Article  MathSciNet  Google Scholar 

  9. I.S. Doubla, Z.T. Njitacke, S. Ekonde et al., Multistability and circuit implementation of tabu learning two-neuron model: application to secure biomedical images in IoMT. Neural Comput. Appl. 33(21), 14945–14973 (2021)

    Article  Google Scholar 

  10. Z.H. Guo, Z.J. Li, M.J. Wang et al., 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  ADS  Google Scholar 

  11. L. Hou, H. Bao, Q. Xu et al., Coexisting infinitely many nonchaotic attractors in a memristive weight-based Tabu learning neuron. Int. J. Bifurc. Chaos. 31(12), 2150189 (2021)

    Article  MathSciNet  Google Scholar 

  12. Z. Huang, C. Yang, X. Zhou et al., Brain-inspired STA for parameter estimation of fractional-order memristor-based chaotic systems. Appl. Intell. 53, 1–13 (2023)

    Article  Google Scholar 

  13. B. Ibarz, J.M. Casado, M.A. Sanjuán, Map-based models in neuronal dynamics. Phys. Rep. 501(1–2), 1–74 (2011)

    Article  ADS  Google Scholar 

  14. Q. Lai, C. Lai, Design and implementation of a new hyperchaotic memristive map. IEEE Trans. Circuits Syst. II Express Briefs 69(4), 2331–2335 (2022)

    Google Scholar 

  15. Q. Lai, L. Yang, Discrete memristor applied to construct neural networks with homogeneous and heterogeneous coexisting attractors. Chaos Solitons Fractals 174, 113807 (2023)

    Article  MathSciNet  Google Scholar 

  16. C. Li, Y. Yang, X. Yang et al., Application of discrete memristors in logistic map and Hindmarsh–Rose neuron. Eur. Phys. J. Special Top. 231(16), 3209–3224 (2022)

    Article  ADS  Google Scholar 

  17. K.X. Li, B.C. Bao, J. Ma et al., Synchronization transitions in a discrete memristor-coupled bi-neuron model. Chaos Solitons Fractals. 165, 112861 (2022)

    Article  Google Scholar 

  18. R. Li, Z. Wang, E. Dong, A new locally active memristive synapse-coupled neuron model. Nonlinear Dyn. 104(4), 4459–4475 (2021)

    Article  Google Scholar 

  19. T. Liu, J. Mou, L. Xiong et al., Hyperchaotic maps of a discrete memristor coupled to trigonometric function. Phys. Scr. 96(12), 125242 (2021)

    Article  ADS  Google Scholar 

  20. Y. Lu, C. Wang, Q. Deng, Rulkov neural network coupled with discrete memristors. Netw. Comput. Neural Syst. 33(3–4), 214–232 (2022)

    Article  Google Scholar 

  21. J. Ma, L. Mi, P. Zhou et al., Phase synchronization between two neurons induced by coupling of electromagnetic field. Appl. Math. Comput. 307, 321–328 (2017)

    MathSciNet  Google Scholar 

  22. F.F. Yang, G.D. Ren, J. Tang, Dynamics in a memristive neuron under an electromagnetic field. Nonlinear Dyn. (2023). https://doi.org/10.1007/s11071-023-08969-8

    Article  Google Scholar 

  23. M.L. Ma, X.H. Xie, Y. Yang et al., Synchronization coexistence in a Rulkov neural network based on locally active discrete memristor. Chin. Phys. B 32(5), 058701 (2023)

    Article  ADS  Google Scholar 

  24. T. Ma, J. Mou, B. Li et al., Study on the complex dynamical behavior of the fractional-order hopfield neural network system and its implementation. Fractal Fractional. 6(11), 637 (2022)

    Article  Google Scholar 

  25. T. Ma, J. Mou, A.-B.A. Abdullah et al., Hidden dynamics of memristor-coupled neurons with multi-stability and multi-transient hyperchaotic behavior. Phys. Scr. 98(10), 105202 (2023)

    Article  ADS  Google Scholar 

  26. M. Ma, K. Xiong, Z. Li et al., Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk. Chin. Phys. B 98(10), 105202 (2023)

    Google Scholar 

  27. Z.T. Njitacke, B.N. Koumetio, B. Ramakrishnan et al., Hamiltonian energy and coexistence of hidden firing patterns from bidirectional coupling between two different neurons. Cognit. Neurodyn. 16(4), 899–916 (2021)

    Article  Google Scholar 

  28. Q. Xu, T. Liu, S. Ding et al., Extreme multistability and phase synchronization in a heterogeneous bi-neuron Rulkov network with memristive electromagnetic induction. Cognit. Neurodyn. 17(3), 755–766 (2023)

    Article  Google Scholar 

  29. M. Chen, D. Guo, T. Wang et al., Bidirectional control of absence seizures by the basal ganglia: a computational evidence. PLoS Comput. Biol. 10(3), 1003495 (2014)

    Article  Google Scholar 

  30. S.S. Muni, K. Rajagopal, A. Karthikeyan et al., Discrete hybrid Izhikevich neuron model: nodal and network behaviours considering electromagnetic flux coupling. Chaos Solitons Fractals 155, 111759 (2022)

    Article  Google Scholar 

  31. Y. Peng, K. Sun, S. He, A discrete memristor model and its application in Hénon map. Chaos Solitons Fractals. 137, 109873 (2020)

    Article  MathSciNet  Google Scholar 

  32. R. Qiu, Y. Dong, X. Jiang et al., Two-neuron based memristive hopfield neural network with synaptic crosstalk. Electronics 11(19), 3034 (2022)

    Article  Google Scholar 

  33. L. Ren, J. Mou, S. Banerjee et al., A hyperchaotic map with a new discrete memristor model: design, dynamical analysis, implementation and application. Chaos Solitons Fractals. 167, 113024 (2023)

    Article  MathSciNet  Google Scholar 

  34. N.F. Rulkov, Modeling of spiking-bursting neural behavior using two-dimensional map. Phys. Rev. E 65(4), 041922 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  35. T. Ma, J. Mou, H. Yan et al., A new class of Hopfield neural network with double memristive synapses and its DSP implementation. Eur. Phys. J. Plus. 137(10), 1–19 (2022)

    Article  Google Scholar 

  36. S. Majhi, M. Perc, D. Ghosh, Chimera states in uncoupled neurons induced by a multilayer structure. Sci. Rep. 6(1), 39033 (2016)

    Article  ADS  Google Scholar 

  37. S.S. Muni, Mode-locked orbits, doubling of invariant curves in discrete Hindmarsh–Rose neuron model. Physica Scripta. 98(8) (2023)

  38. F.F. Yang, Q. Guo, J. Ma, A neuron model with nonlinear membranes. Cognit. Neurodyn. 1–12 (2023)

  39. H. Lin, C. Wang F. Yu, et al., A triple-memristor hopfield neural network with space multi-structure attractors and space initial-offset behaviors. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. (2023)

  40. S. Zhang, J. Zheng, X. Wang et al., Initial offset boosting coexisting attractors in memristive multi-double-scroll Hopfield neural network. Nonlinear Dyn. 102(4), 2821–2841 (2020)

    Article  Google Scholar 

  41. H. Lin, C. Wang, J. Sun et al., Memristor-coupled asymmetric neural networks: bionic modeling, chaotic dynamics analysis and encryption application. Chaos Solitons Fractals. 166, 112905 (2023)

    Article  MathSciNet  Google Scholar 

  42. M. Ma, Y. Yang, Z. Qiu et al., A locally active discrete memristor model and its application in a hyperchaotic map. Nonlinear Dyn. 107(3), 2935–2949 (2022)

    Article  Google Scholar 

  43. L. Zhang, Y. Wang, X. Leng et al., Analysis of neural network connections based on memristors and their multiple offset phenomena. Phys. Scr. 98(11), 2023 (2023)

    Article  Google Scholar 

Download references

Acknowledgements

National Natural Science Foundation of China under Grant No. 62061014

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Contributions

Miao Wang designed and carried out experiments, data analyzed and manuscript wrote. Jun Mou and Hadi Jahanshahi made the theoretical guidance for this paper. Lei Qin improved the algorithm. All authors reviewed the manuscript.

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Correspondence to Jun Mou.

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Wang, M., Mou, J., Qin, L. et al. A memristor-coupled heterogeneous discrete neural networks with infinite multi-structure hyperchaotic attractors. Eur. Phys. J. Plus 138, 1137 (2023). https://doi.org/10.1140/epjp/s13360-023-04772-x

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