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Dynamic analysis and hardware implementation of multi-scroll Hopfield neural networks with three different memristor synapses

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Abstract

Neurons play an important role in forming behaviors and cognition through synaptic interactions. When organized into neural networks, these neurons can exhibit complex dynamic behaviors, such as multi-scroll and hyperchaotic attractors. In this study, we investigated the dynamic behavior of memristor synapses between four small neurons and proposed a new segmented linear memristor. Based on this, an improved version of the second memristor was obtained by modification. Subsequently, a new neural network was constructed, and the coefficients of the neural network were slightly adjusted. Two memristor synapse HNNs were constructed separately. Finally, these memristors were integrated as synapses and autapses to create the third memristive synapse HNN. It is worth noting that the last memristive HNN can generate hyperchaotic multi-scroll attractors, and its memristor function effectively controls the number of scroll axes. The dynamics of the hyperchaotic multi-scroll memristive HNN were analyzed using phase diagrams, bifurcation diagrams, Poincare maps, and Lyapunov exponent plots. In terms of hardware implementation, we used FPGA to implement the proposed hyperchaotic multi-scroll model and demonstrated 6 memristive HNN attractors on an oscilloscope to validate the accuracy of the model. Finally, a simple image encryption scheme with high information entropy was designed, demonstrating good encryption effectiveness.

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Acknowledgements

This work was supported by the Natural Science Foundation of Hunan Province under Grants 2022JJ30624 and 2022JJ10052; the Scientific Research Fund of Hunan Provincial Education Department under grant 21B0345; the National Natural Science Foundation of China under Grant 62172058; and the Postgraduate Training Innovation Base Construction Project of Hunan Province under Grant 2020-172-48.

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Authors and Affiliations

  1. School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, 410114, China

    Fei Yu, Chaoran Wu, Yue Lin, Shaoqi He, Wei Yao & Shuo Cai

  2. School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, 411201, China

    Jie Jin

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  1. Fei Yu
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by [Fei Yu], [Chaoran Wu], and [Yue Lin]. The first draft of the manuscript was written by [Chaoran Wu] and [Fei Yu], and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Datasets generated and/or analyzed during the current study may be obtained from the corresponding authors upon reasonable request.

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Yu, F., Wu, C., Lin, Y. et al. Dynamic analysis and hardware implementation of multi-scroll Hopfield neural networks with three different memristor synapses. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09614-8

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