Equivalence of phase-oscillator and integrate-and-fire models.

Journal: Physical review. E, Statistical, nonlinear, and soft matter physics
Published Date:

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

  • Antonio Politi
    Institute for Complex Systems and Mathematical Biology and SUPA, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom.
  • Michael Rosenblum
    Department of Physics and Astronomy, University of Potsdam, Karl-Libknecht-Strasse 24/25, 14476 Potsdam, Germany.