Modeling scale-free neurodynamics using neuropercolation approach

Critical properties of dynamical models of neural populations are studied. Based on the classical work of Renyi-Erdos on the evolution of random graphs, a new class of random cellular automata models called neuropercolation has been introduced. We show the emergence of phase transitions in neuropercolation models at critical combination of several control parameters, including the level of external gain and noise, the density of long-range axonal connections (small-world phenomenon), and the sparseness of feedback between excitatory and inhibitory neural populations. Noise level and structural properties of the cortical tissue has been used to control the critical exponent, starting from white noise (slope 0) far away from criticality. The results show that scale-free power spectral density characterizes the dynamics near criticality, where exponent with a power exponent approaching -2. The results are interpreted in the context of recent experimental findings on the dynamics and structure of the cortex.