Analysis Of Neural Oscillation In Neural Population Using Describing Function Method

Neural Mass Model (NMM) is a high-order nonlinear model contained essential non-linear function (Sigmoid nonlinear function). The S function play an important role in regulating activities of Neural Mass Model, further more, which is the root of generating limit cycle oscillation in NMM. Describing function method is an effective method to analyze the limit cycle oscillation characteristics of nonlinear system, and is used to research the stability of nonlinear control systems in the field of frequency domain. The main requirement employing describing function method, to analyze nonlinear system lie in that the linear part of the system has low pass filtering property. Since NMM is a high-order system, which means it has a good low pass filtering properties, thus the analysis accuracy using describing function method should be satisfactory.ObjectiveUnder the theoretical framework of describing function approach, theoretical analysis of the spontaneous oscillation characteristics of NMM is conducted, and the oscillation frequencies are determined. Neural oscillation plays a key role in the transmission of neural information. Theoretical analysis can not only determine their oscillation characteristics, but also gain insight into the influence of parameters on the oscillation characteristics of NMM, further more to reveal the mechanism of spontaneous oscillation of NMM.MethodsThis paper analyzes simple, classic and multi-dynamic NMM using describing function method, respectively. The analysis process mainly includes the following three parts:Firstly, the model transformation is conducted to derive a typical structure composed of linear and nonlinear parts.Secondly, the curve of negatively reciprocal describing function and Nyquist plot of linear part is drawn, respectively. The cross point of the two curves means that spontaneous oscillation occurs, and the stable one represents spontaneous oscillation of NMMFinally, simulation model of NMM is constructed, and simulations verify the accuracy of theoretical analysis results.ResultsThrough describing function analysis, spontaneous oscillation characteristics of three kinds of NMM are determined, respectively. We can derive the following results through describing function analysis of NMM:1. The method of linearization of NMM at its center point can gained accurate frequency characteristic, but gained lager amplitude characteristic.2. The harmonic linearization method can gain not only accurate frequency characteristic but also accurate amplitude characteristic.3. Describing function method can qualitatively analyze the frequency characteristic of Multi-dynamic NMM.Simulation results verify the efficiency of theoretical analysis.This study reveals and elucidates the mechanism of spontaneous oscillation of NMM from the information science view point.