ALTERNATING OSCILLATORY AND STOCHASTIC DYNAMICS IN A MODEL FOR A NEURONAL ASSEMBLY

In recent neurophysiological experiments stimulus-related neuronal osc illations were discovered in various species. The oscillations are not persistent during the whole time of stimulation, but instead seem to be restricted to rather short periods, interrupted by stochastic perio ds. In this contribution we argue, that these observations can be expl ained by a bistability in the ensemble dynamics of coupled integrate a nd fire neurons. This dynamics can be cast in terms of a high-dimensio nal map for the time evolution of a phase density which represents the ensemble state. A numerical analysis of this map reveals the coexiste nce of two stationary states in a broad parameter regime when the syna ptic transmission is nonlinear. The one state corresponds to a stochas tic firing of individual neurons, the other state describes a periodic activation. We demonstrate that under the influence of additional ext ernal noise the system can switch between these states, in this way re producing the experimentally observed activity. We also investigate th e connection between the nonlinearity of the synaptic transmission fun ction and the bistability of the dynamics. To this purpose we heuristi cally reduce the high-dimensional assembly dynamics to a one-dimension al map, which in turn yields a simple explanation for the relation bet ween nonlinearity and bistability in our system.