title: Phase transition to frequency entrainment in a long chain of pulse-coupled oscillators.
abstract: A long chain of pulse-coupled oscillators was studied. The oscillators interacted via a phase response curve similar to those obtained from pacemaker cells in the heart. The natural frequencies were random numbers from a distribution with finite bandwidth. Stable frequency-entrained states were shown always to exist above a critical coupling strength. Below the critical coupling, the probability to have such states was shown to be zero if the number of oscillators is infinite. This discontinuity establishes the existence of a phase transition in the thermodynamic limit. For weak coupling, clusters of frequency-entrained oscillators emerged. The cluster sizes were exponentially distributed, even when the critical coupling was approached. At this coupling, the mean cluster size diverged to infinity according to a power law. The standard deviation of the distribution of mean frequencies in the chain converged to zero, also according to a power law.
authors.affiliation: Department of Mathematical Physics, Lund University, S-221 00 Lund, Sweden. per.ostborn@matfys.lth.se
authors.forename: Per
authors.initials: P
authors.lastname: Ostborn