Activity-dependent model for neuronal avalanches

Networks of living neurons represent one of the most fascinating systems of modem biology. If the physical and chemical mechanisms at the basis of the functioning of a single neuron are quite well understood, the collective behavior of a system of many neurons is an extremely intriguing subject. Crucial ingredient of this complex behavior is the plasticity property of the network, namely the capacity to adapt and evolve depending on the level of activity. This plastic ability is believed, nowadays, to be at the basis of learning and memory in real brains. This fundamental problem in neurobiology has recently shown a number of features in common to other complex systems. These features mainly concern the morphology of the network, namely the spatial organization of the established connections, and a novel kind of neuronal activity. Experimental data have, in fact, shown that electrical information propagates in a cortex slice via an avalanche mode. Both features have been found in other problems in the context of the physics of complex systems and successful models have been developed to describe their behavior. In this contribution, we apply a statistical mechanical model to describe the complex activity in a neuronal network. The network is chosen to have a number of connections in long range, as found for neurons in vitro. The model implements the main physiological properties of living neurons and is able to reproduce recent experimental results. The numerical power spectra for electrical activity reproduces also the power law behavior measured in an EEG of man resting with the eyes closed.