Criticality in probabilistic models of spreading dynamics in brain networks: Epileptic seizures
Fig 6
Phase diagrams derived from mean-field approximations.
Top row: phase diagrams were obtained from exact continuous time simulations (temporal Gillespie algorithm) of the proposed probabilistic model on ER networks of different sizes N = 1024, 4096, 8192. Red curves indicate the boundary between no-spread and spread phases estimated via mean-field finite-size corrected approximations. Black curves denote the boundary separating the no-seizure phase from the other two phases derived from the mean-field approximations. Bottom row: phase diagrams obtained by the simulation of the mean-field dynamics approximation in discrete-time (Eqs 26, 27 and 28; see also Materials and methods). Red and black curves are the transition boundaries derived from the mean-field approximation without the finite-size correction. As the network size grows, the agreement between the two (top and bottom) phase diagrams improves as expected.