Open AccessSpontaneous oscillation analysis of neural mass model using describing function approach
Author(s) -
Wang Jun-Song,
Yanguang Xu
Publication year - 2014
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.63.068701
Subject(s) - oscillation (cell signaling) , sigmoid function , nonlinear system , physics , describing function , function (biology) , artificial neural network , control theory (sociology) , statistical physics , computer science , quantum mechanics , artificial intelligence , evolutionary biology , biology , genetics , control (management)
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.