中文摘要：

以感应电场作用下的Morris-Lecar（ML）神经元模型为研究对象,研究了ML神经元的平衡态及稳定性。首先基于感应电场引起的膜极化电压ΔV的变化,给出了三类神经元的平衡态及其分岔行为。通过引入转换相图与平衡曲线,揭示了感应电场作用下神经元的放电机制。结果发现：分岔可引起神经元膜电压V绕平衡曲线运动,并产生簇发放电、峰放电、阈下放电现象。同时,在周期性正弦感应电场的激励下,神经元模型可产生不同的周期放电模式。极低频电磁场激励下的神元放电机制可为电磁场治疗神经疾病提供一定的理论参考,对大脑认知有潜在的应用价值。

英文摘要：

This paper presents the equilibrium and stability of Morris-Lecar（ML） neuron model exposed to induced electric field. Based on the variation of the field-induced membrane depolarization, the equilibrium and bifurcation behaviors of three basic classes of neurons are investigated. The discharge mechanism of neurons simulated by electromagnetic fields is revealed by introducing transformed phase portraits with the equilibrium curve. Results show that bifurcations can lead to the movement of neuronal membrane potential V around the equilibrium eurve, and different types of firing patterns, including bursting, synchronous spiking and sub-threshold oscillations. Meanwhile, neurons exhibit different kinds of periodic firing patterns in the simulation of periodic sinusoidal induced electric field. The study can provide theoretical reference for the extremely low frequency electromagnetic field in treating neurologieal diseases, and has potential application value for the brain cognitive.