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Discrete memristor applied to construct neural networks with homogeneous and heterogeneous coexisting attractors

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  • Lai, Qiang
  • Yang, Liang

Abstract

Memristors are widely used to simulate the effects of electromagnetic radiation on neurons or as synapses to simulate excitation and inhibition between neurons. This paper constructs discrete neural network models (DNNMs) in three scenarios: without discrete memristor, discrete memristor simulate electromagnetic radiation stimulation, and discrete local active memristor simulate synapses. Research reveals that the DNNM without fixed points under electromagnetic radiation stimulation, which in turn induces hidden hyperchaotic attractors and also observes the existence of infinite coexisting homogeneous attractors. Meanwhile, the DNNM can generate heterogeneous coexisting attractors after introducing a memristor to mimic synapses. Numerical results show that discrete memristors can induce the DNNM to develop more complex chaotic dynamics. In addition, a hardware platform is designed to validate the numerical results, and the DNNMs are applied to construct the pseudo-random number generator (PRNG).

Suggested Citation

  • Lai, Qiang & Yang, Liang, 2023. "Discrete memristor applied to construct neural networks with homogeneous and heterogeneous coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007087
    DOI: 10.1016/j.chaos.2023.113807
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    7. Minglin Ma & Kangling Xiong & Zhijun Li & Yichuang Sun, 2023. "Dynamic Behavior Analysis and Synchronization of Memristor-Coupled Heterogeneous Discrete Neural Networks," Mathematics, MDPI, vol. 11(2), pages 1-13, January.
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    Cited by:

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    5. Wang, Qiao & Tian, Zean & Wu, Xianming & Li, Kunshuai & Sang, Haiwei & Yu, Xiong, 2024. "A 5D super-extreme-multistability hyperchaotic map based on parallel-cascaded memristors," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    6. Ding, Dawei & Jin, Fan & Zhang, Hongwei & Yang, Zongli & Chen, Siqi & Zhu, Haifei & Xu, Xinyue & Liu, Xiang, 2024. "Fractional-order heterogeneous neuron network based on coupled locally-active memristors and its application in image encryption and hiding," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    7. Jia, Junen & Wang, Chunni & Zhang, Xiaofeng & Zhu, Zhigang, 2024. "Energy and self-adaption in a memristive map neuron," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    8. Wang, Chunhua & Li, Yufei & Deng, Quanli, 2025. "Discrete-time fractional-order local active memristor-based Hopfield neural network and its FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    9. Hu, Jingting & Bao, Han & Xu, Quan & Chen, Mo & Bao, Bocheng, 2024. "Synchronization generations and transitions in two map-based neurons coupled with locally active memristor," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    10. Wan, Qiuzhen & Yang, Qiao & Liu, Tieqiao & Chen, Chaoyue & Shen, Kun, 2024. "Single direction, grid and spatial multi-scroll attractors in Hopfield neural network with the variable number memristive self-connected synapses," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    11. Ma, Tao & Mou, Jun & Chen, Wanzhong, 2025. "Enriched dynamical behavior of a novel locally active memristor-driven neuron map," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    12. Qin, Bo & Zhang, Ying, 2024. "Comprehensive analysis of the mechanism of sensitivity to initial conditions and fractal basins of attraction in a novel variable-distance magnetic pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    13. Zhu, Wanting & Sun, Kehui & Wang, Huihai & Fu, Longxiang & Minati, Ludovico, 2024. "Dynamics, synchronization and analog circuit implementation of a discrete neuron-like map with pulsating spiral dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    14. Wan, Qiuzhen & Chen, Chaoyue & Liu, Tieqiao & Rao, Huhui & Dong, Jun, 2025. "High-dimensional memristor-coupled multiple neural networks with spatial multi-structure attractors and application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    15. Zhou, Mingjie & Li, Guodong & Pan, Hepeng & Song, Xiaoming, 2025. "Discrete memristive hyperchaotic map with heterogeneous and homogeneous multistability and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    16. Bashkirtseva, I. & Ryashko, L., 2024. "Dynamical variability, order-chaos transitions, and bursting Canards in the memristive Rulkov neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    17. Chai, Xiuli & Shang, Guangyu & Wang, Binjie & Gan, Zhihua & Zhang, Wenkai, 2024. "Exploiting 2D-SDMCHM and matching embedding driven by flag-shaped hexagon prediction for visually meaningful medical image cryptosystem," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    18. Wang, Chunhua & Luo, Dingwei & Deng, Quanli & Yang, Gang, 2024. "Dynamics analysis and FPGA implementation of discrete memristive cellular neural network with heterogeneous activation functions," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).

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