Fig. 6: Heterogeneous mean-field analysis of the Brusselator model.
From: Amplitude death and restoration in networks of oscillators with random-walk diffusion
a Phase space for the stationary solution \(({x}_{j}^{(0)},{y}_{j}^{(0)})\), j = 1, …, N. Red circles correspond to the fixed point for diffusion value D = 2 as obtained from solving system (4). Black squares correspond to the mean-field result for the same D. b Eigenvalue spectra resulting from stability analysis. Red circles correspond to the eigenvalues λj, j = 1, …, 2N, of the original fixed point for each for D = 2, whereas open black squares indicate the spectra resulting from the mean-field reduction. c Mean-field value of the y variable, \(\overline{y}\), for the fixed point. Results obtained from directly solving system (4) (red continuous curve), and from the mean-field reduction (black dashed curve). d Largest eigenvalue’s real part for the mean-field solution with ER networks with average degree 〈k〉 = 20 (red), 30 (blue), 40 (green), and 50 (purple). For each set of networks each line denotes a different network size. From top to bottom, N = 103, 104, 105, and 106.
