Criticality in probabilistic models of spreading dynamics in brain networks: Epileptic seizures
Fig 10
Power-law divergence of response functions and
near the critical point.
We used finite-size scaling analysis over four different network sizes of 213, 214, 215, 216. A The expected value of the normalized spread size, ψ = 〈s/N〉, as a function of w (fixed E) near the critical point (wc ≈ 6.76 10−5, Ec ≈ 1.00 10−6). The inset zooms the view around the critical point. B The response χw plotted as a function of w (for fixed E = Ec). The inset shows the divergence of the maximum response χw,m as a function of χw,m ∼ N0.16(1). C,D The log-scale plots show the power-law behavior of the response function χw as w approaches the critical point from below with corresponding scaling χw− ∼ (wc − w)β′−1 and exponent estimated as , and from above with corresponding scaling χw+ ∼ (w − wc)β−1 and exponent estimated as
. E The expected value of the normalized spread size, as a function of E near the critical point (for fixed w = wc). F The response χE plotted as a function of E (for fixed w = wc). The inset shows the divergence of the maximum response χw,m as a function of χw,m ∼ N0.18(1). G,H The log-scale plots show the power-law behavior of the response χE as E approaches the critical point from below with corresponding scaling χE− ∼ (Ec − E)1/δ′−1 and exponent estimated as
, and from above with corresponding scaling χE+ ∼ (E − Ec)1/δ−1 and exponent estimated as
.