Spontaneous oscillation analysis of neural mass model using describing function approach

Abstract

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 oscillation 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 spontaneous 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.