title: Collective phase response curves for heterogeneous coupled oscillators.
abstract: Phase response curves (PRCs) have become an indispensable tool in understanding the entrainment and synchronization of biological oscillators. However, biological oscillators are often found in large coupled heterogeneous systems and the variable of physiological importance is the collective rhythm resulting from an aggregation of the individual oscillations. To study this phenomena we consider phase resetting of the collective rhythm for large ensembles of globally coupled Sakaguchi-Kuramoto oscillators. Making use of Ott-Antonsen theory we derive an asymptotically valid analytic formula for the collective PRC. A result of this analysis is a characteristic scaling for the change in the amplitude and entrainment points for the collective PRC compared to the individual oscillator PRC. We support the analytical findings with numerical evidence and demonstrate the applicability of the theory to large ensembles of coupled neuronal oscillators.
authors.affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA.
authors.forename: Kevin M
authors.initials: KM
authors.lastname: Hannay
authors.affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA.|Department of Anesthesiology, University of Michigan, Ann Arbor, Michigan 48109, USA.
authors.forename: Victoria
authors.initials: V
authors.lastname: Booth
authors.affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA.|Center for Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, Michigan 48109, USA.
authors.forename: Daniel B
authors.initials: DB
authors.lastname: Forger
mesh_terms: D000200:Action Potentials; D001683:Biological Clocks / Q000502:physiology; D003198:Computer Simulation; D008954:Models, Biological; D009474:Neurons / Q000502:physiology