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Memristive electromagnetic induction effects on Hopfield neural network

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Abstract

Due to the existence of membrane potential differences, the electromagnetic induction flows can be induced in the interconnected neurons of Hopfield neural network (HNN). To express the induction flows, this paper presents a unified memristive HNN model using hyperbolic-type memristors to link neurons. By employing theoretical analysis along with multiple numerical methods, we explore the electromagnetic induction effects on the memristive HNN with three neurons. Three cases are classified and discussed. When using one memristor to link two neurons bidirectionally, the coexisting bifurcation behaviors and extreme events are disclosed with respect to the memristor coupling strength. When using two memristors to link three neurons, the antimonotonicity phenomena of periodic and chaotic bubbles are yielded, and the initial-related extreme events are emerged. When using three memristors to link three neurons end to end, the extreme events owning prominent riddled basins of attraction are demonstrated. In addition, we develop the printed circuit board (PCB)-based hardware experiments by synthesizing the memristive HNN, and the experimental results well confirm the memristive electromagnetic induction effects. Certainly, the PCB-based implementation will benefit the integrated circuit design for large-scale Hopfield neural network in the future.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos. 61971228 and 51777016, the Natural Science Foundation of Henan Province under Grant No. 202300410351, and the Key Scientific Research of Colleges and Universities in Henan Province under Grant No. 21A120007.

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Authors and Affiliations

  1. School of Electrical and Automation Engineering and School of Computer Science and Technology, Nanjing Normal University, Nanjing, 210023, China

    Chengjie Chen & Fuhong Min

  2. School of Information Engineering, Xuchang University, Xuchang, 461000, China

    Yunzhen Zhang

  3. School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164, China

    Bocheng Bao

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  1. Chengjie Chen
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Correspondence to Fuhong Min.

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Chen, C., Min, F., Zhang, Y. et al. Memristive electromagnetic induction effects on Hopfield neural network. Nonlinear Dyn 106, 2559–2576 (2021). https://doi.org/10.1007/s11071-021-06910-5

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