Brain complexity and phase transitions

I shall briefly describe studies in our group of mathematical models for brain
cooperative functions and network structure. They concern the propagation of
weak signals, states of attention and growth of structure, and illustrate how
the combination of familiar concepts of physics such as chaotic dynamics, non-
equilibrium states, phase transitions and criticality may provide a coherent
understanding of some of the brain complex behaviour. As a by-product, it
follows a convenient definition of complexity, a concept that born among
physicists and mathematician now permeates the scientific development in
biology, chemistry, economy, geology and sociology.