中文摘要：

通过对分数阶FitzHugh-Nagumo模型神经元的研究,当外加电流强度作为分岔参数时,发现这种模型神经元从静息态到周期放电态所经历的Hopf分岔点不同于相应的整数阶模型神经元的分岔点;而且分数阶FitzHugh-Nagumo模型神经元呈现周期放电的外加电流强度的范围比相应的整数阶模型神经元的范围小,然而放电频率却比相应的整数阶模型神经元的放电频率高.同时还揭示在周期放电的情况下分数阶FitzHugh-Nagumo模型神经元之间的同步速率比相应的整数阶模型神经元之间的同步速率快.在数值模拟分数阶微分方程时,采用了精度高、速度快的Adomian分解算法.

英文摘要：

Through the research on the fractional-order FitzHugh-Nagumo model neuron,it is found that the Hopf bifurcation point of the fractional-order model,where the state of the model neuron changes from quiescence to periodic spiking,is different from that of the corresponding integer-order model when the externally applied current is considered as the bifurcation parameter. We further demonstrate that the range of the strength of the externally applied current in the fractional-order model neuron,which can make the model neuron exhibit periodic spiki ng,is smaller than that in the corresponding integer-order model neuron. However,the firing frequency of the fractional-order model neuron is higher than that of the integer-order counterpart. Meanwhile,we show that the synchronization rate of two electrically coupled fractional-order FitzHugh-Nagumo model neurons is greater than that of the integer-order counterpart. The Adomian decompos ition method is employed to calculate fractional-order differential equations numerically because of its rapid convergence and high accuracy.