Stability and spectra of randomly connected excitatory cortical networks

The stability and dispersion spectrum of random excitatory networks of brain components is investigated using a physiological model of brain electrical activity. Stability is shown to sharply constrain the structural parameters of these networks, with a critical point that limits the product of network size, connection probability, and connection strength. This constraint is verified numerically and also has a weak effect on network symmetry. Experimentally determined cortical networks, having a structure intermediate between regular and random networks, are shown to be less stable than a random network with a similar number of components and connections.