title: Phase resetting and coupling of noisy neural oscillators.
abstract: A number of experimental groups have recently computed Phase Response Curves (PRCs) for neurons. There is a great deal of noise in the data. We apply methods from stochastic nonlinear dynamics to coupled noisy phase-resetting maps and obtain the invariant density of phase distributions. By exploiting the special structure of PRCs, we obtain some approximations for the invariant distributions. Comparisons to Monte-Carlo simulations are made. We show how phase-dependence of the noise can move the peak of the invariant density away from the peak expected from the analysis of the deterministic system and thus lead to noise-induced bifurcations.
authors.affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA. bard@math.pitt.edu
authors.forename: Bard
authors.initials: B
authors.lastname: Ermentrout
authors.forename: David
authors.initials: D
authors.lastname: Saunders
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D016477:Artifacts; D001683:Biological Clocks / Q000502:physiology*; D001921:Brain / Q000502:physiology*; D006801:Humans; D008959:Models, Neurological; D009010:Monte Carlo Method; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D009434:Neural Pathways / Q000502:physiology*; D017711:Nonlinear Dynamics; D013269:Stochastic Processes; D009435:Synaptic Transmission / Q000502:physiology*