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Bursting hierarchy in an adaptive exponential integrate-and-fire network synchronization

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Abstract

Neuronal network synchronization has received wide interest. In the present manuscript, we study the influence of initial membrane potentials together with network topology on bursting synchronization, in particular the sequential order of stabilized bursting among neurons. We find a hierarchical phenomenon on their bursting order. With a focus on situations where network coupling advances spiking times of neurons, we grade neurons into different layers. Together with the neuronal network structure, we construct directed graphs to indicate bursting propagation between different layers. More explicitly, neurons in upper layers burst earlier than those in lower layers. More interestingly, we find that among the same layer, bursting order of neurons is mainly associated with the number of neurons they connected to the upper layer; more stimuli lead to earlier bursting. Receiving effectively the same stimuli from the upper layer, we observe neurons with fewer connections would burst earlier.

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Acknowledgements

C.L. acknowledges financial support from National Natural Science Foundation of China (NSFC, Grant Nos. 12171179 and 11871061) and Natural Science Foundation of Hubei Province (Grant No. 2020CFB847). Y.Z. is supported by NSFC Grant Nos. 12161141002 and 11871262 and Hubei Key Laboratory of Engineering Modeling and Scientific Computing. The authors would like to thank the anonymous reviewers for their constructive comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China

    Congping Lin, Xiaoyue Wu & Yiwei Zhang

  2. Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China

    Congping Lin & Yiwei Zhang

  3. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China

    Congping Lin & Yiwei Zhang

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  1. Congping Lin
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Correspondence to Yiwei Zhang.

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Communicated by Benjamin Lindner.

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Lin, C., Wu, X. & Zhang, Y. Bursting hierarchy in an adaptive exponential integrate-and-fire network synchronization. Biol Cybern 116, 545–556 (2022). https://doi.org/10.1007/s00422-022-00942-9

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