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

Antonio Politi, M. Rosenblum

Research output: Contribution to journalArticle

15 Citations (Scopus)
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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.
Original languageEnglish
Article number042916
Number of pages11
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume91
Early online date29 Apr 2015
DOIs
Publication statusPublished - 2015

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Integrate
oscillators
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Weak Coupling
pulses
Model
synchronism
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curves
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Cite this

Equivalence of phase-oscillator and integrate-and-fire models. / Politi, Antonio; Rosenblum, M.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 91, 042916, 2015.

Research output: Contribution to journalArticle

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AB - 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.

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