NEURONAL NETWORKS WITH SPONTANEOUS, CORRELATED BURSTING ACTIVITY - THEORY AND SIMULATIONS

A model of spontaneously active biological neuronal networks is proposed where each component neuron is an excitable dynamical unit of the Hodgkin-Huxley (HH) type described by a system of ordinary differential equations. Neurotransmitter fluxes are additional state variables in such networks and the action of chemical synapses is modelled by additional kinetic equations. Networks composed of intrinsically inactive units may ignite to one or more correlated bursting patterns. These transitions can be described as bifurcations governed by interaction parameters. Stability problems and classes of synchronized solutions are studied. Networks of this type exhibit rich dynamics (multiple attractors), including the possibility of Synchronized chaotic activity. Biological and information processing applications are reviewed and some open mathematical problems are indicated.