中文摘要：

文章提出在外部周期刺激和噪声共同作用下全局耦合神经振子集群的相位演化模型,引入平均数密度描述神经振子集群的整体活动,利用Fokker-Planck方程导出了平均数密度的演化方程。数值模拟结果表明：刺激对神经振子群同步活动的影响取决于刺激强度和刺激频率;当刺激频率比系统特征频率小很多或者大得多时,神经振子集群的数密度呈现减幅振荡行为;当刺激频率接近系统特征频率时,神经振子集群趋于完全同步;在相同刺激频率条件下,神经振子集群的同步程度与刺激强度有关,刺激越强同步程度越高。

英文摘要：

A phase model of globally coupled neuronal oscillator population in the presence of external periodic stimulus and noise is proposed, and the evolution equation of average number density describing the overall activity of neuronal population is derived with the Fokker-Planck equation. The results of numerical simulations indicate that the impact of stimulus on synchronization of a population of neuronal oscillators depends on stimulation intensity and stimulation frequency. If the stimulus frequency is much smaller or larger than the characteristic frequency of system, the number density of neuronal population shows a damped oscillation behavior. If the stimulus frequency is close to the characteristic frequency of system, the neuronal population tends to complete synchronization. As the stimulus frequency is fixed, stimulus with stronger intensity leads to higher synchronization.