How Oscillatory Neuronal Responses Reflect Bistability and Switching of the Hidden Assembly Dynamics

Part of Advances in Neural Information Processing Systems 5 (NIPS 1992)

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K. Pawelzik, H.-U. Bauer, J. Deppisch, T. Geisel


A switching between apparently coherent (oscillatory) and stochastic episodes of activity has been observed in responses from cat and monkey visual cortex. We describe the dynamics of these phenomena in two paral(cid:173) lel approaches, a phenomenological and a rather microscopic one. On the one hand we analyze neuronal responses in terms of a hidden state model (HSM). The parameters of this model are extracted directly from exper(cid:173) imental spike trains. They characterize the underlying dynamics as well as the coupling of individual neurons to the network. This phenomenolog(cid:173) ical model thus provides a new framework for the experimental analysis of network dynamics. The application of this method to multi unit ac(cid:173) tivities from the visual cortex of the cat substantiates the existence of oscillatory and stochastic states and quantifies the switching behaviour in the assembly dynamics. On the other hand we start from the single spiking neuron and derive a master equation for the time evolution of the assembly state which we represent by a phase density. This phase density dynamics (PDD) exhibits costability of two attractors, a limit cycle, and a fixed point when synaptic interaction is nonlinear. External fluctuations can switch the bistable system from one state to the other. Finally we show, that the two approaches are mutually consistent and therefore both explain the detailed time structure in the data.