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Symmetric multi-double-scroll attractors in Hopfield neural network under pulse controlled memristor

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Investigating the chaotic dynamics in neural networks holds significant importance in elucidating brain-like neural activities and guiding brain-like learning. The multi-scroll chaos, due to its intricate topological structure, has garnered interest in the study of brain-like chaotic neural networks. Previous researches have primarily focused on ordinary multi-scroll attractors, while there has been little research on symmetric multi-scroll attractors. Symmetric attractors are typically more diverse and have more flexible evolutionary and higher stability which may lead to more stable system responses. The purpose of this paper is to investigate the symmetric multi-scroll phenomenon generated under the influence of the memristor controlled by multi-level-logic pulse in Hopfield Neural Network (HNN). Firstly, a memristive HNN capable of generating multi-scroll is proposed, serving as the foundation for studying the influence of multi-level-logic pulse. Through theoretical and numerical analysis, the dynamic behavior of the proposed memristive HNN is examined and simulation results reveal the emergence of multi-scroll attractors and initial offset coexisting behavior. Subsequently, a multi-level-logic pulse is introduced into the memristor to simulate one of its parameters. The experimental results reveal that the introduction of multi-level-logic pulse expands the original multi-scroll structure into a symmetric structure. Furthermore, it enlarges the chaotic parameter range of the system, which holds significant implications for the study of neural dynamics. Finally, the correctness of the proposed model is verified through hardware experiments. This study provides valuable guidance for neural dynamics researches and the application of memristors.

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This work is supported by the National Natural Science Foundation of China (No.62271197) and Guangdong Basic and Applied Basic Research Foundation (No.2024A1515011910)


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J.L wrote the main manuscript text. J.L and C.W made formal analysis, methodology. Q.D made resources, software and data curation. J.L made investigation, validation and visualization. C.W made funding acquisition. All authors reviewed the manuscript.

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Correspondence to Chunhua Wang.

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Li, J., Wang, C. & Deng, Q. Symmetric multi-double-scroll attractors in Hopfield neural network under pulse controlled memristor. Nonlinear Dyn (2024).

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