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: 2026-04-27
Accepted Date: 2026-06-29
Rev Recd Date: 2026-06-28

Available Online: 2026-07-14

Abstract

Abstract

Objective In recent years, memristors have been employed to emulate neuronal synapses with dynamically adjustable synaptic weights, enabling the construction of Memristive Hopfield Neural Networks (HNNs). Compared with conventional HNNs, Memristive HNNs more accurately reproduce the nonlinear dynamical behavior of biological neural systems. Multi-scroll attractors have attracted considerable attention in secure communication because of their complex topological structures and strong state-space ergodicity. However, previous studies have primarily focused on conventional multi-scroll attractors with single structural patterns, whereas multi-scroll attractors with special structures remain largely unexplored. Therefore, this paper proposes a nested multi-scroll Memristive HNN system that generates nested multi-scroll attractors, thereby overcoming the limitations of conventional single-structure multi-scroll attractors. Methods A Four-Dimensional (4D) Memristive HNN system is constructed from a three-neuron HNN by incorporating a multi-segment nonlinear magnetically controlled memristor into the Memristive self-connected synapse of neuron 2. Equilibrium-point and stability analyses are performed to investigate the regulatory effects of the Memristive self-connected synapse coupling strength and system initial conditions on the system dynamics. The number of multi-scroll attractors is regulated by adjusting the memristor control parameters. Building on this framework, a Multi-level Logic Pulse current (I_MLP) is introduced to construct a nested multi-scroll Memristive HNN system. The proposed system generates nested multi-scroll attractors with enhanced dynamical complexity. Finally, the MATLAB numerical simulation results are validated through Multisim circuit simulations and Field-Programmable Gate Array (FPGA)-based hardware experiments. Results and Discussions The results demonstrate that regulating the Memristive self-connected synapse coupling strength enables the proposed 4D Memristive HNN system to exhibit period-doubling bifurcations and chaotic behavior, as illustrated by the bifurcation diagrams and Lyapunov exponent spectra (Fig. 3). Various types of coexisting attractors are generated under different coupling strengths (Fig. 4). By adjusting the memristor control parameters, multi-scroll attractors with different numbers of scrolls are generated through one-directional extension (Figs. 5～8). After the introduction of the I_MLP, the proposed nested multi-scroll Memristive HNN system generates nested multi-scroll attractors while preserving the controllable scroll-number extension property (Figs. 8～10). Spectral Entropy (SE) analysis demonstrates that the I_MLP increases the dynamical complexity of the proposed system compared with the original 4D Memristive HNN system (Figs. 9 and 10). The strong agreement among MATLAB numerical simulations, Multisim circuit simulations, and FPGA-based hardware experiments confirms the physical realizability of the proposed nested multi-scroll Memristive HNN system (Figs. 12～14). Conclusions A 4D Memristive HNN system is constructed by incorporating a multi-segment nonlinear magnetically controlled memristor into the Memristive self-connected synapse of a three-neuron HNN. Equilibrium-point and stability analyses reveal the regulatory effects of the Memristive self-connected synapse coupling strength and the evolution of coexisting attractors associated with different initial conditions. The results show that the system enters chaos through the period-doubling route to chaos and generates single-scroll and double-scroll chaotic attractors. The number of multi-scroll attractors is continuously increased by adjusting the memristor control parameters. Furthermore, introducing the I_MLP produces a nested multi-scroll Memristive HNN system capable of generating nested multi-scroll attractors with increased dynamical complexity. The strong agreement among MATLAB numerical simulations, Multisim circuit simulations, and FPGA-based hardware experiments validates the physical realizability of the proposed nested multi-scroll Memristive HNN system.

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References(16)

References

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