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Dynamical transitions of the coupled Class I (II) neurons regulated by an astrocyte

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Abstract

Based on the minimal neural network models consisting of a pyramidal (PY) neuron, an interneuron (IN), and an astrocyte (AS), we investigate the regulating effects of astrocyte on dynamical transitions in two coupled neurons of the same type of excitability, either Class I or Class II, which is characterized by saddle-node on invariant circle (SNIC) and Hopf (HB) bifurcation, respectively. It is found that without the regulation of AS, the coupled Class I PY and IN neurons show the regular \(L^s\) mixed-mode oscillations (MMOs) composed of L large amplitude oscillations (LAOs) and s small amplitude oscillations (SAOs) in one period. Under the AS action, the calcium signals in AS can induce and regulate the mixed-mode low-frequency bursting firings. By contrast, for the coupled Class II PY and IN neurons, when AS is ignored, as the coupling strength increases, the system shows the periodic LAO oscillations, \(L^s\) mode of oscillations, and the chaotic behaviors. Furthermore, the period-doubling bifurcation is clearly captured. However, the presence of AS makes the PY neuron exhibit the mixed-mode low-frequency chaotic bursting activities. Interestingly, we also discover a new transition route (\(1^0\rightarrow 1^1\rightarrow 1^2\rightarrow \ldots \)) of calcium signals due to the period adding bifurcation of the system, which can shape the firing patterns of the PY neuron. Our results suggest that calcium signals in AS indeed involve in and even shape the coupling dynamics of PY and IN neurons. In particular, AS may exert differential roles in modulating the dynamical properties of Class I and Class II neurons.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants No. 11932003).

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Authors and Affiliations

  1. Department of Dynamics and Control, Beihang University, Beijing, 100191, China

    Jinyi Zhao, Qishao Wang & Qingyun Wang

  2. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Denggui Fan

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Zhao, J., Fan, D., Wang, Q. et al. Dynamical transitions of the coupled Class I (II) neurons regulated by an astrocyte. Nonlinear Dyn 103, 913–924 (2021). https://doi.org/10.1007/s11071-020-06122-3

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