A Nested Multi-scroll Memristive Hopfield Neural Network and Its Hardware Implementation

WANG Zhe; WAN Qiuzhen; ZHOU Pan; RAO Huhui

doi:10.11999/JEIT260516

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WANG Zhe, WAN Qiuzhen, ZHOU Pan, RAO Huhui. A Nested Multi-scroll Memristive Hopfield Neural Network and Its Hardware Implementation[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260516

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WANG Zhe, WAN Qiuzhen, ZHOU Pan, RAO Huhui. A Nested Multi-scroll Memristive Hopfield Neural Network and Its Hardware Implementation[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260516

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A Nested Multi-scroll Memristive Hopfield Neural Network and Its Hardware Implementation

doi: 10.11999/JEIT260516 cstr: 32379.14.JEIT260516

College of Information Science and Engineering, Hunan Normal University, Changsha 410081, China

Funds: The National Natural Science Foundation of China (61901169), The Natural Science Foundation of Hunan Province (2024JJ5267)

Received Date: 2026-04-26
Accepted Date: 2026-06-29
Rev Recd Date: 2026-06-28

Available Online: 2026-07-14

Abstract

Abstract

Objective In recent years, researchers have employed memristors to simulate neuronal synapses for dynamically adjusting synaptic weights, thereby constructing memristive neural networks. The memristive Hopfield neural network (HNN) can more precisely reflect the nonlinear dynamic behavior of biological neural systems. Notably, multi-scroll attractors have garnered significant attention in the field of secure communication owing to their complex topological structures and high state-space ergodicity. However, most existing studies have focused primarily on single-structure multi-scroll attractors, whereas multi-scroll attractors with special structures remain in need of further exploration. Consequently, this paper proposes an HNN system capable of generating special nested multi-scroll attractors, thereby overcoming the limitations of traditional single-structure multi-scroll attractors. Methods A four-dimensional (4D) memristive HNN system is constructed based on a three-neuron HNN. In this system, a multi-segment nonlinear magnetically controlled memristor is integrated into the self-connected synapse of neuron 2. By analyzing the equilibrium points and system stability, this study investigates the effects of memristor coupling strength and system initial conditions. The number of multi-scroll attractors can be increased by adjusting the parameters of the memristor. Building upon this, a novel nested multi-scroll memristive HNN system is established by introducing multi-level logic pulse current. The proposed system can generate unique nested multi-scroll attractors, and its complexity can be further enhanced. Finally, the accuracy of the MATLAB numerical results is verified through Multisim circuit simulation and FPGA-based hardware experiments. Results and Discussions The experimental results indicate that by regulating the coupling strength of the memristor self-connected synapses, the proposed 4D memristive HNN system can yield bifurcation diagrams and Lyapunov exponent spectra (Fig. 3), as well as diverse coexisting attractors (Fig. 4). Meanwhile, multi-scroll attractors with varying scroll numbers are obtained (Fig. 5–7). By regulating multi-level logic pulse currents, a novel nested multi-scroll memristive HNN system is constructed. This system can generate nested multi-scroll attractors (Fig. 9–10). Spectral entropy analysis demonstrates that, compared with the original 4D memristive HNN system, the proposed system has its complexity effectively enhanced (Fig. 11–12). Both Multisim simulation (Fig. 14) and FPGA-based experiments (Fig. 15–16) verify the feasibility of the proposed memristive HNN system. Conclusions Based on a three-neuron HNN, a 4D memristive HNN system is constructed by embedding a multi-segment nonlinear magnetically controlled memristor. Through equilibrium point and stability analysis, this paper reveals the regulatory effect of the memristor coupling strength, as well as the evolution law of coexisting attractors dependent on initial conditions. The results show that the system can enter a chaotic state via a period-doubling bifurcation route and produce single-scroll and double-scroll chaotic attractors. The number of multi-scroll attractors can be increased by optimizing memristor parameters. Furthermore, by regulating multi-level logic pulse currents, a novel nested multi-scroll memristive HNN system is developed to generate nested multi-scroll attractors. Spectral entropy analysis proves that the application of multi-level logic pulse currents enhances the system complexity. The numerical simulation results from MATLAB, Multisim simulations and FPGA-based experimental results are highly consistent, which validates the feasibility of the nested multi-scroll memristive HNN system.
- Hopfield neural network,
- Memristive self-connecting synapses,
- Multi-level logic pulse current,
- Nested multi-scroll attractor,
- Hardware implementation.

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References(16)

References

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