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.

• Received 13 March 2013

DOI:https://doi.org/10.1103/PhysRevLett.110.204101