Spectral characteristics of the dynamical core of the human brain. To generate a heterogeneous brain network model (i.e. with different dynamics at each node), we optimized each single bifurcation parameter independently by fitting for each value of global coupling G the spectral characteristics of the simulated and empirical BOLD signals at each brain area. (A) The evolution of the fitting of the FC and FCD statistics as a function of G. For large enough value of the global coupling a good fitting of both is obtained, i.e. large correlation between the empirical and simulated grand average FC and low difference in the statistics of the empirical and simulated FCD (Kolmogorov-Smirnov distance). (B) The evolution of the single values of the local bifurcations parameters as a function of the global coupling G. For low values of G homogeneous local bifurcation parameters around zero are obtained. When the level of fitting improves for larger values of G a more heterogeneous distribution of is obtained. (C) The local bifurcation parameters for each region for the uncoupled network (i.e. G = 0) and for the optimal coupling (G = 5.4). If the network is uncoupled, each single brain area fitted the spectral characteristics of the empirical BOLD signals in a very homogeneous way by local bifurcations parameters at the edge of the local Hopf bifurcation, i.e. at zero. (D) When the whole-brain network is coupled, we can discover the “true” intrinsic local dynamics that fits the local empirical BOLD characteristics and the global quantities FC, FCD and metastability.