Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method

doi:10.1088/1674-1056/27/4/048701

Abstract

Spontaneous alpha oscillations are a ubiquitous phenomenon in the brain and play a key role in neural information processing and various cognitive functions. Jansen's neural mass model (NMM) was initially proposed to study the origin of alpha oscillations. Most of previous studies of the spontaneous alpha oscillations in the NMM were conducted using numerical methods. In this study, we aim to propose an analytical approach using the describing function method to elucidate the spontaneous alpha oscillation mechanism in the NMM. First, the sigmoid nonlinear function in the NMM is approximated by its describing function, allowing us to reformulate the NMM and derive its standard form composed of one nonlinear part and one linear part. Second, by conducting a theoretical analysis, we can assess whether or not the spontaneous alpha oscillation would occur in the NMM and, furthermore, accurately determine its amplitude and frequency. The results reveal analytically that the interaction between linearity and nonlinearity of the NMM plays a key role in generating the spontaneous alpha oscillations. Furthermore, strong nonlinearity and large linear strength are required to generate the spontaneous alpha oscillations.

Keywords: neural mass model spontaneous alpha oscillation describing function

Received: 01 November 2017
Revised: 07 January 2018
Accepted manuscript online:

PACS:	87.10.-e	(General theory and mathematical aspects)
	87.18.Sn	(Neural networks and synaptic communication)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund:

Project supported by the National Natural Science Foundation of China (Grant No. 61473208), the Tianjin Research Program of Application Foundation and Advanced Technology, China (Grant No. 15JCYBJC47700), the National Institutes of Health, USA (Grant Nos. R01DA040990 and R01EY027544), and the Project of Humanities and Social Sciences from the Ministry of Education, China (Grant No. 17YJAZH092).

Corresponding Authors: Jun-Song Wang
E-mail: wjsong2004@126.com

Cite this article:

Yao Xu(徐瑶), Chun-Hui Zhang(张春会), Ernst Niebur, Jun-Song Wang(王俊松) Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method 2018 Chin. Phys. B 27 048701

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Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method

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