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

Xu Yao^{1, 2}, Zhang Chun-Hui¹, Niebur Ernst³, Wang Jun-Song^{1, †}

(color online) Block diagrams of the reformulated NMM using the describing function method. Panel (a) is a reformulated form of the NMM shown in Fig. 1 and is derived by replacing the nonlinear function S(v) using its describing function N(A). Panel (a) is further transformed into panel (b) by approximating the two describing functions N(A) in the excitatory and the inhibitory feedback loops. Panel (c) is an equivalently transformed version of panel (b), where G(s) is the transfer function of the linear part of the NMM (blue dashed rectangle) and N(A) is the nonlinear part of the NMM.