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An electronic implementation for Morris–Lecar neuron model

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Abstract

In this paper, the threshold dynamics of Morris–Lecar neuron model is firstly analyzed by bifurcation diagram of interspike interval as a function of external forcing current, and then the discharge series, phase portraits and nullclines of the neuron under different conditions are investigated in a numerical way. The results show that the electrical activities, such as quiescent state, spiking and bursting, can be observed when the values of external forcing current beyond certain thresholds. Finally, based on the 2-D nonlinear differential equations of Morris–Lecar neuron model, a complete electronic implementation of this model is proposed and studied in detail. At the same time, a circuitry realization of the hyperbolic cosine function \(\tau _W (V)\) in the Morris–Lecar neuron model is put forward and described carefully. The outputs of designed circuits are consistent well with the theoretical predictions, which validate the design methods. Moreover, the circuit presented in this paper can be used as an experimental unit to investigate the dynamics of a single neuron or collective behaviors of a large-scale neural network.

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Acknowledgments

The authors thank the anonymous referees for their very constructive and helpful suggestions. This work is partially supported by the National Nature Science Foundation of China under the Grant Nos. 51177117 and 51307130.

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Authors and Affiliations

  1. State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an, 710049, China

    Xiaoyu Hu, Chongxin Liu, Ling Liu, Junkang Ni & Shilei Li

  2. School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Xiaoyu Hu, Chongxin Liu, Ling Liu, Junkang Ni & Shilei Li

Authors
  1. Xiaoyu Hu
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  2. Chongxin Liu
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  3. Ling Liu
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Correspondence to Xiaoyu Hu.

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Hu, X., Liu, C., Liu, L. et al. An electronic implementation for Morris–Lecar neuron model. Nonlinear Dyn 84, 2317–2332 (2016). https://doi.org/10.1007/s11071-016-2647-y

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  • DOI: https://doi.org/10.1007/s11071-016-2647-y

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