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

Received Date: 2025-09-24
Accepted Date: 2025-12-01
Rev Recd Date: 2025-11-30

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, producing highly nonlinear dynamics. Developing artificial neural network models and analyzing them with nonlinear dynamics theory is therefore of considerable scientific and practical interest. As a brain-inspired model, the Hopfield Neural Network (HNN) exhibits more diverse dynamics when a Memristor Hopfield Neural Network (MHNN) is formed by introducing a memristor into its structure. Among such systems, networks that generate Multi-Double Scroll (MDS) attractors are advantageous because their richer dynamical behavior and more complex topological structure offer strong potential for applications such as image encryption.Methods: A memristor model based on an arctangent-function series is proposed and introduced into a fully connected HNN. This forms an MHNN that incorporates electromagnetic radiation effects and memristive synaptic weights. The mechanism responsible for generating MDS chaotic attractors is examined through equilibrium-point analysis. Dynamical characteristics, including the effects of memristive synaptic coupling strength and initial offset boosting, are evaluated using bifurcation diagrams, Lyapunov-exponent spectra, and attraction basins. The system is then implemented on an FPGA platform.Results and Discussions: The MHNN generates an arbitrary number of multi-directional MDS chaotic attractors (Figs. 4, 5, 6). Adjusting the memristive synaptic coupling strength yields distinct coexisting attractor types (Figs. 7, 8). Multiple coexisting MDS chaotic attractors also emerge from modifications of the initial values (Figs. 9, 10, 11, 12). Hardware implementation on an FPGA (Figs. 13, 14) confirms the correctness and feasibility of the system.Conclusions: The proposed MHNN generates unidirectional, bidirectional, and tridirectional MDS chaotic attractors in phase space. The number of scrolls is tuned by the memristor control parameter. The system also shows initial offset boosting, and the number of coexisting attractors is regulated by this parameter. Higher-dimensional networks can be constructed by increasing the number of memristive synapses, demonstrating the broad generality of the model. Owing to its complex topology and rich dynamics, the network offers promising potential for engineering applications.
- Memristive Hopfield neural network,
- Multi-Double Scroll (MDS) attractor,
- Initial offset boosting,
- FPGA hardware implementation

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