< Back to Article

Criticality in probabilistic models of spreading dynamics in brain networks: Epileptic seizures

Fig 9

Power-law divergence of stochastic fluctuations in spread size near the critical point.

We used finite-size scaling analysis over four different network sizes of 2¹³, 2¹⁴, 2¹⁵, 2¹⁶. A The standard-deviation σ of the fluctuations as a function of w (fixed E = E_c) near the critical point (w_c ≈ 6.7610⁻⁵, E_c ≈ 1.0010⁻⁶). The inset shows the power-law divergence of σ at its maximum and the corresponding scaling σ_m ∼ N^0.66(1). B,C Power-law behavior of σ shown on log-scale for w approaching the critical point from below with corresponding scaling and exponent estimated as , and from above with corresponding scaling σ₊ ∼ (w − w_c)^−γ and exponent estimated as , respectively. D The standard-deviation σ of the fluctuations as a function of E (fixed w = w_c) near the critical point. The inset shows the power-law divergence of σ at its maximum and the corresponding scaling σ_m ∼ N^0.68(1). G,H Power-law behavior of σ(E) shown on log-scale for E approaching the critical point from below with corresponding scaling and exponent estimated as , and from above with corresponding scaling σ₊ ∼ (E − E_c)^−α and exponent estimated as .

doi: https://doi.org/10.1371/journal.pcbi.1010852.g009