title: Weakly coupled oscillators in a slowly varying world.
abstract: We extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a pair of oscillators. We apply this to the simple Hopf oscillator and then to a biophysical model. The latter represents the behavior of a neuron that is subject to slow modulation of a muscarinic current such as would occur during transient attention through cholinergic activation. Our method extends and simplifies the recent work of Kurebayashi (Physical Review Letters, 111, 214101, 2013) to include coupling. We apply the method to an all-to-all network and show that there is a waxing and waning of synchrony of modulated neurons.
authors.affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA. yop6@pitt.edu.
authors.forename: Youngmin
authors.initials: Y
authors.lastname: Park
authors.affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA.
authors.forename: Bard
authors.initials: B
authors.lastname: Ermentrout
mesh_terms: D001703:Biophysics; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D010507:Periodicity
keywords: Modulation; Oscillators; Slowly varying parameters; Traub model; Weak coupling