An electronic implementation for Morris–Lecar neuron model

• DOI: 10.1007/s11071-016-2647-y
• Publication Date: 2016-02-23T05:54:51Z
• Authors: Xiaoyu Hu; Chongxin Liu; Ling Liu; Junkang Ni; Shilei Li
• Keywords: Biological neuron model; Phase portrait; Bursting; Realization (probability); Representation; Forcing (mathematics)

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.