Alternating Oscillatory and Stochastic Dynamics in a Model for a Neuronal Assembly

In recent neurophysiological experiments stimulus-related neuronal oscillations 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 periods. In this contribution we argue, that these observations can be explained by a bistability in the ensemble dynamics of coupled integrate and re neurons. This dynamics can be cast in terms of a high-dimensional map for the time evolution of a phase density which represents the ensemble state. A numerical analysis of this map reveals the coexistence of two stationary states in a broad parameter regime when the synaptic transmission is nonlinear. The one state corresponds to a stochastic ring of individual neurons, the other state describes a periodic activation. We demonstrate that under the in uence of additional external noise the system can swich between these states, in this way reproducing the experimentally observed activity. We also investigate the connection between the nonlinearity of the synaptic transmission function and the bistability of the dynamics. To this purpose we heuristically reduce the high dimensional assembly dynamics to a one-dimensional map, which in turn yields a simple explanantion for the relation between nonlinearity and bistability in our system. 2