中文摘要：

在无外界刺激时神经群表现为节律性自激振荡,自激振荡是非线性系统特有的一种运动形式。在非线性描述函数法理论框架下,对神经群模型自激振荡特性进行分析,并揭示其产生机理。神经群模型的sigmoid非线性函数（简称为S函数）是其自激振荡的根源。首先,求解S函数的描述函数；然后,基于S函数的描述函数得到神经群模型正反馈回路S函数和负反馈回路S函数的等效增益,在此基础上将神经群模型转化为可用描述函数法分析的典型结构形式；最后,应用描述函数法理论对神经群模型自激振荡特性进行理论分析,得到自激振荡特性的定量描述,并通过仿真分析对理论分析结果进行了验证。理论分析及仿真分析结果表明基于描述函数方法的神经群自激振荡特性分析方法是正确有效的。 S 函数是神经系统的典型非线性环节,S函数的处理方法及神经群自激振荡特性分析方法对于其他神经模型的自激振荡特性分析具有参考价值。

英文摘要：

Neural mass model （NMM） can generate spontaneous oscillation even in a resting state. However, it remains little known which mechanism is responsible for NMM’s spontaneous oscillation. From dynamical theory, spontaneous oscilla-tion is an intrinsic property of nonlinear system, which means that the sigmoid nonlinear function （S function） of NMM plays a key role in the emergence of its spontaneous oscillation. In this study, describing function approach is employed to analyze the spontaneous oscillation characteristics of a kind of extended NMM. Firstly, the describing function of S function is derived, through which the two S functions in excitatory and inhibitory feedback loop, respectively, are approximated. Secondly, the NMM is transformed into a typical block diagram composed of a nonlinear unit and a linear unit. Thirdly, in the theoretical framework of describing function approach, theoretical analysis of the sponta-neous oscillation characteristics of NMM is conducted, and the oscillation frequencies are determined. The simulation results demonstrate that the theoretical results are correct and the employed approach is effective. Since S function exists extensively in neural system, the proposed approach has a potential application in the spontaneous oscillation analysis of other neural model.