Array enhanced stochastic resonance and spatio-temporal synchronization
A.R. Bulsara
Naval Command, Control and Ocean Surveillance Center, RDT & E Division,
San Diego, CA 92152-5000, USA
We consider the interpretation of time series data from firing events in periodically stimulated sensory neurons. Theoretical models, representing the neurons as nonlinear dynamic switching elements subject to deterministic (taken to be time-periodic) subthreshold signals buried in a Gaussian noise background, are developed. The models considered include simple bistable dynamics which provide a good description of the noise-induced cooperative behavior in neurons on a statistical or coarse-grained level, but do not account for many important features (e.g. capacitative effects) of real neuron behavior, as well as very simple "integrate-fire" models which provide reasonable descriptions of capacitative behavior but attempt to duplicate refractoriness only through the boundary conditions on the dynamics. Cooperative effects, e.g. "stochastic resonance", arising through the interplay of the noise and deterministic modulation, are examined, together with their possible implications in the features of Inter-Spike-Interval Histograms (ISIHs). Experimental data which points to the existence of stochastic resonance as a mechanism in the processing of sub-threshold signals in the nervous system, will be presented. We also explore the connection between stochastic resonance, usually defined at the level of the power spectral density of the response, and the cooperative behavior observed in the ISIH.
Finally, we present some very recent results on cooperative phenomena that occur in networks of nonlinear dynamic elements with global or local coupling; the coupling may, in turn, be linear or nonlinear. It is shown that, in the presence of a subthreshold deterministic signal (taken to be time-periodic),the noise (or the coupling) may synchronize the array dynamics on a global scale. The synchronized state may be precisely connected to a synchronous escape rate of two events per cycle of the sinusoidal driving signal. The connection of this behavior to stochastic resonance in the network, and its signal processing implications are discussed.