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Discrete-time fractional-order local active memristor-based Hopfield neural network and its FPGA implementation

Author

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  • Wang, Chunhua
  • Li, Yufei
  • Deng, Quanli

Abstract

In this paper, a fractional-order discrete-time Hopfield neural network (HNN) with three neurons is studied, and discrete-time fractional-order local active memristor is used as the mutual synapses and electromagnetic radiation of HNN neurons respectively. Chaotic dynamic characteristics of the entire four-dimensional fractional discrete-time system are analyzed, including Li’s index, phase diagram, bifurcation diagram analysis. The results show that the system has attractor coexistence, multi-stability phenomena and other, which proves its complex dynamic characteristics. In addition, the truncation method is applied to the caputo operator for the first time to realize the discrete fractional order system with FPGA, and the results are shown.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:193:y:2025:i:c:s0960077925000669
    DOI: 10.1016/j.chaos.2025.116053
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    References listed on IDEAS

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    1. Chunhua Wang & Yufei Li & Gang Yang & Quanli Deng, 2025. "A Review of Fractional-Order Chaotic Systems of Memristive Neural Networks," Mathematics, MDPI, vol. 13(10), pages 1-22, May.
    2. Luo, Min & Wang, Pingli & Qiu, Da & Zhang, Bo & Liu, Song, 2025. "Analysis and application of conditionally symmetric memristive chaotic systems with attractor growth phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).
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    5. Yang, Liu & Zhang, Jie, 2025. "Memristor-coupled heterogeneous Hopfield neural network with switchable activation functions and its synchronization control," Chaos, Solitons & Fractals, Elsevier, vol. 200(P3).
    6. Wang, Binchi & Ren, Guodong & Ma, Jun & Guo, Yitong, 2025. "A memristive neuron with double capacitive variables coupled by Josephson junction," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    7. 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).
    8. Zang, Hongyan & Huang, Lili & Gao, Fei & Lei, Tengfei & Dong, Yujiao & Wang, Guangyi, 2025. "Memristor neurons with symmetric activity on the edge of chaos: Mono-/biphasic complex neuromorphic behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 201(P3).

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