title: Analysis of synchronization in a slowly changing environment: how slow coupling becomes fast weak coupling.
abstract: Many physical and biological oscillators are coupled indirectly through a slowly evolving dynamic medium. We present a perturbation method that shows that slow dynamics of a coupling medium is effectively equivalent to weak coupling of oscillators. Our methods first apply the theory of averaging to obtain a periodic solution to a single system and then exploit small fluctuations around the mean to analyze coupling between systems. We use this method to explain the spike-to-spike asynchrony seen in a model for bursting neurons coupled through extracellular potassium and to explore synchronization in a model for quorum sensing.
authors.affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.
authors.forename: Jonathan J
authors.initials: JJ
authors.lastname: Rubin
authors.affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.
authors.forename: Jonathan E
authors.initials: JE
authors.lastname: Rubin
authors.affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.
authors.forename: G Bard
authors.initials: GB
authors.lastname: Ermentrout