title: Equivalence of phase-oscillator and integrate-and-fire models.
abstract: A quantitative comparison of various classes of oscillators (integrate-and-fire, Winfree, and Kuramoto-Daido type) is performed in the weak-coupling limit for a fully connected network of identical units. An almost perfect agreement is found, with only tiny differences among the models. We also show that the regime of self-consistent partial synchronization is rather general and can be observed for arbitrarily small coupling strength in any model class. As a byproduct of our study, we are able to show that an integrate-and-fire model with a generic pulse shape can be always transformed into a similar model with δ pulses and a suitable phase response curve.
authors.affiliation: Institute for Complex Systems and Mathematical Biology and SUPA, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.
authors.forename: Antonio
authors.initials: A
authors.lastname: Politi
authors.affiliation: Department of Physics and Astronomy, University of Potsdam, Karl-Libknecht-Strasse 24/25, 14476 Potsdam, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Rosenblum
mesh_terms: D016571:Neural Networks, Computer