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) Analytical results of the spontaneous alpha oscillations in the NMM using the describing function method. (a) Analytical results. The blue curve denotes the Nyquist diagram of the linear part G ( j ω ) , where the array represents the increase of angular frequency ω. The red line refers to the negative reciprocal of the describing function of sigmoid function S(v), which is calculated as − 1 / N ( A ) . Intersection between the blue curve and the red line corresponds to the spontaneous oscillation in the NMM. (b) Simulation results of the spontaneous alpha oscillations in the NMM. (c) A comparison between analytical and simulation results.