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.