Modeling and Dynamic Analysis of Controllable Multi-Double Scroll Memristor Hopfield Neural Network

LIU Song; LI Zihan; QIU Da; LUO Min; LAI Qiang

doi:10.11999/JEIT250972

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LIU Song, LI Zihan, QIU Da, LUO Min, LAI Qiang. Modeling and Dynamic Analysis of Controllable Multi-Double Scroll Memristor Hopfield Neural Network[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250972

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LIU Song, LI Zihan, QIU Da, LUO Min, LAI Qiang. Modeling and Dynamic Analysis of Controllable Multi-Double Scroll Memristor Hopfield Neural Network[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250972

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Modeling and Dynamic Analysis of Controllable Multi-Double Scroll Memristor Hopfield Neural Network

doi: 10.11999/JEIT250972 cstr: 32379.14.JEIT250972

LIU Song^{1
,
,},
LI Zihan¹,
QIU Da¹,
LUO Min¹,
LAI Qiang²

1.
School of College of Intelligent Systems Science and Engineering, Hubei Minzu University, Enshi 445000, China
2.
School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China

Funds: Natural Science Foundation of Hubei Province of China (2024AFD068), the Fund of China University Research Innovation (2024IT115)

Accepted Date: 2025-12-01
Rev Recd Date: 2025-12-01

Available Online: 2025-12-09

Abstract

Abstract

Objective:The human brain is a complex neural system capable of integrated information storage, computation, and parallel processing. The collective activity of neuronal populations processes and coordinates sensory inputs, resulting in highly nonlinear dynamics. Therefore, developing artificial neural network models and analyzing them with nonlinear dynamics theories is of considerable scientific and practical importance. As a brain-inspired model, the Hopfield neural network (HNN) can exhibit more diverse dynamics when a memristor is incorporated into its structure. Among various memristive neural networks, those generating multi-scroll attractors are particularly advantageous due to their richer dynamical behaviors and more complex topological structures, granting them significant research value and application potential in fields such as image encryption.Methods: A memristor model based on an arctangent function series is proposed and introduced into a fully connected HNN. This constructs a class of memristive HNNs that incorporate electromagnetic radiation effects and memristive synaptic weights. The generation mechanism of multi-double-scroll chaotic attractors is verified through equilibrium point analysis. Dynamical characteristics, including the effects of memristive synaptic coupling strength and initial offset-boosting behavior, are investigated using bifurcation diagrams, Lyapunov exponent spectra, and attraction basins. Finally, the system is implemented on an FPGA platform.Results and Discussions:This class of memristive HNN is capable of generating an arbitrary number of multi-directional multi-double-scroll chaotic attractors (Figs. 4, 5, 6). By adjusting the memristive synaptic coupling strength, various distinct types of coexisting attractors are observed (Figs. 7, 8). Furthermore, multiple coexisting multi-double-scroll chaotic attractors are revealed through modifications of the initial values (Figs. 9, 10, 11, 12). Finally, the hardware implementation on an FPGA (Figs. 13, 14) verifies the correctness and feasibility of the system.Conclusions:The findings indicate that the proposed model can generate unidirectional, bidirectional, and tridirectional multi-double-scroll chaotic attractors in phase space. The number of scrolls is precisely adjustable via the memristor’s control parameter. The system also exhibits initial-offset-boosting behavior, where the number of coexisting attractors is likewise regulated by this parameter. A higher-dimensional network can be constructed by increasing the number of memristive synapses, demonstrating the considerable universality of the proposed system. Benefiting from its intricate topology and rich dynamics, this network holds promising application prospects in engineering fields.
- Memristive neural network,
- Multi-Double-Scroll attractor,
- Initial offset boosting,
- FPGA hardware implementation

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References(30)

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