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Grid multi-double-scroll attractors in a magnetized Hopfield neural network with a memristive self-connection synapse

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Grid multi-scroll attractors possess distinctive properties in complex topologies and functions, yet their generation mechanisms in the neural networks still need further exploration. This paper presents a novel method to generate the grid multi-double-scroll attractors within the neural networks. Firstly, a new magnetized Hopfield neural network (HNN) model under the influence of electromagnetic radiation is developed. This model utilizes an electromagnetic radiation control method based on a multi-piecewise memristor to efficiently regulate the number of single direction multi-double-scroll attractors. Secondly, the above proposed magnetized HNN model combined with a memristive self-connection synapse is constructed by using another multi-piecewise memristor to simulate the autapse of a neuron. This combined HNN model with the double multi-piecewise memristors demonstrates the grid multi-double-scroll attractors and the initial-offset behaviors. Finally, the feasibility of the proposed magnetized HNN model is verified by the FPGA platform.

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The datasets generated and/or analyzed during the current study are available from the corresponding author on a reasonable request.


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The authors would like to thank the project supported by the National Natural Science Foundation of China under Grants 61901169 and 61804037, and the Natural Science Foundation of Hunan Province under Grant 2024JJ5267.


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Authors and Affiliations



QW: Conceptualization, validation, supervision, writing, resources, funding acquisition. SC: Investigation, methodology, data curation, writing. TL: Investigation, software, visualization. CC: Investigation, software. QY: Methodology, software.

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Correspondence to Qiuzhen Wan.

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Wan, Q., Chen, S., Liu, T. et al. Grid multi-double-scroll attractors in a magnetized Hopfield neural network with a memristive self-connection synapse. Nonlinear Dyn 112, 14513–14526 (2024).

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