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Grid multi-scroll attractors in memristive Hopfield neural network under pulse current stimulation and multi-piecewise memristor

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Abstract

Grid multi-scroll attractors are widely studied in the traditional chaotic systems but are rarely appeared in the neural network systems. This paper proposes a novel method for generating the grid multi-scroll attractors based on a memristive Hopfield neural network (HNN). Firstly, the mathematical model of a simple memristive HNN is developed with an original memristor as a connecting synapse, and its equilibrium points and dynamic behaviors are analyzed. Then, a pulse-controlled memristive HNN is constructed when an external multi-level-logic pulse current is applied to one neuron. Theoretical analysis and numerical simulations reveal that an appropriate external pulse current stimulation can stabilize the chaotic HNN by inducing a dynamic transition from chaotic to weakly chaotic and then to periodic behavior. Additionally, by introducing a multi-piecewise memristor into the pulse-controlled memristive HNN, this study demonstrates that the various complex grid multi-scroll attractors can be generated. By setting the different series of multi-level-logic pulse currents and multi-piecewise memristor control parameters, the structure of the grid multi-scroll attractors can be controlled, including multi-double-scroll, multi-three-scroll and multi-four-scroll attractors. Finally, a physical circuit implementing the grid multi-scroll attractors is presented using the basic commercial electronic components. The proposed approach has the potential to be applied in the treatment of neurological diseases.

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Data availability

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

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Acknowledgments

The authors would like to thank the project supported by the National Natural Science Foundation of China (Grant No. 61901169) and the Natural Science Foundation of Hunan Province, China (Grant No. 2019JJ40190).

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Correspondence to Qiuzhen Wan.

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Wan, Q., Chen, S., Yang, Q. et al. Grid multi-scroll attractors in memristive Hopfield neural network under pulse current stimulation and multi-piecewise memristor. Nonlinear Dyn 111, 18505–18521 (2023). https://doi.org/10.1007/s11071-023-08834-8

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