Noise-induced phenomena in electrically coupled neuronal networks

Electrical coupling is known to be a mechanism for signal propagation between cells. On the example of two different biological models we demonstrate other important effects that coupling has on the dynamics of the network. We consider the electrically coupled network of LC neurons and present analytical and numerical results supporting the hypothesis that coupling promotes synchronization and enhances the fidelity of responses of LC neurons to the various stimuli. On the example of the model of pancreatic β-cells we explain the striking difference in cell behavior observed in various experimental environments. Using the tools from bifurcation theory, perturbation theory, and Wentzell-Freidlin theory of large deviations, we analyze how the effect of the combination of small perturbation and electrical coupling depends on the unique properties of underlying deterministic models.Ph.D., Mathematics -- Drexel University, 201