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Firing activities analysis of a novel small heterogeneous coupled network through a memristive synapse

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Abstract

The heterogeneous coupled network has shown its research values in brain science and bionics. In this paper, a novel small heterogeneous coupled network through a memristive synapse is proposed and investigated. The model is constructed by coupling a 2D Hindmarsh–Rose (HR) neuron with a 3D Hopfield neural network (HNN) through a memristive synapse. Subsequently, the complex dynamical behaviors exhibited by the network were investigated. Specifically, we varied the coupling parameter k12 of the 3D HNN and found that the membrane potentials of the 2D HR neuron possess seven stable firing patterns. Then, by varying the coupling parameter k1 between the 2D HR neuron and the 3D HNN, the membrane potentials of the 2D HR neuron generated five stable firing patterns. Furthermore, by fixing the coupling parameters and varying the initial values of the network, multistability behavior was exhibited by the network. These findings have potential applications in brain science and bionics. Finally, a circuit is designed to realize the network in both simulation and experiments.

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Data availability

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

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 62071411) and the Research Foundation of Education Department of Hunan Province, China (Grant No.20B567).

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Authors and Affiliations

  1. School of Automation and Electronic Information, Xiangtan University, Xiangtan, 411105, People’s Republic of China

    Mengjiao Wang, Jiwei Peng & Zhijun Li

  2. School of Electrical, Electronic and Computer Engineering, University of Western Australia, Crawley, WA, 6009, Australia

    Xinan Zhang & Herbert Ho-Ching Iu

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  1. Mengjiao Wang
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  2. Jiwei Peng
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  3. Xinan Zhang
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  4. Herbert Ho-Ching Iu
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Correspondence to Mengjiao Wang.

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Wang, M., Peng, J., Zhang, X. et al. Firing activities analysis of a novel small heterogeneous coupled network through a memristive synapse. Nonlinear Dyn 111, 15397–15415 (2023). https://doi.org/10.1007/s11071-023-08626-0

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