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Multi-time scale dynamics of mixed depolarization block bursting

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Abstract

Two-coupled excitatory neurons model containing both calcium-activated non-specific cationic and persistent sodium current in the pre-Bötzinger complex (pre-BötC) is studied. A new type of mixed burst similar to a depolarization block bursting (DB-bursting) is observed in the model of pre-BötC neurons. The multi-time scale dynamics, one- and two-parameter bifurcation analysis, are used to study the types of mixed burst and their transition mechanisms. The results show that the periodic fluctuation of calcium concentration has a great influence on the generation of mixed bursting. The change of time scale caused by fluctuation of calcium concentration and the relative position of bifurcation curves have great influence on patterns of bursting.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11872003), Cultivation Plan for “Yujie” Team of North China University of Technology (No. 107051360019XN137/002).

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Authors and Affiliations

  1. College of Science, North China University of Technology, Beijing, 100144, China

    Lixia Duan, Tongtong Liang & Yaqi Zhao

  2. Department of Mathematics, University of Texas at Arlington, Arlington, TX, 76019, USA

    Hongguang Xi

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  1. Lixia Duan
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  2. Tongtong Liang
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Correspondence to Lixia Duan.

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Appendix

Appendix

For \(x\in \{mp,m,h,n,s\}\), the function of \(x_{\infty }(V)\) takes the form \(x_{\infty }(V)=\{1+exp(V-\theta _{x}/\sigma _{x})\}^{-1}\). For \(x\in \{h,n,s\}\), the function of \(\tau _{x}(V)\) takes the form \(\tau _{x}(V)= {\bar{\tau }}_{x}/\cosh [(V-\theta _{x})/2\sigma _{x}]\). The parameter values are shown in Table 1.

Table 1 Parameter values used in the model
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Duan, L., Liang, T., Zhao, Y. et al. Multi-time scale dynamics of mixed depolarization block bursting. Nonlinear Dyn 103, 1043–1053 (2021). https://doi.org/10.1007/s11071-020-05744-x

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