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Phase transition to frequency entrainment in a long chain of pulse-coupled oscillators

Östborn, Per LU (2002) In Physical Review E 66(1).
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review E
volume
66
issue
1
publisher
American Physical Society
external identifiers
  • wos:000177200600018
  • scopus:41349093319
ISSN
1063-651X
DOI
10.1103/PhysRevE.66.016105
language
English
LU publication?
yes
id
d172cee8-1245-433e-9be0-370e821468a9 (old id 331891)
date added to LUP
2007-11-08 08:45:01
date last changed
2017-12-10 04:33:52
@article{d172cee8-1245-433e-9be0-370e821468a9,
  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.},
  author       = {Östborn, Per},
  issn         = {1063-651X},
  language     = {eng},
  number       = {1},
  publisher    = {American Physical Society},
  series       = {Physical Review E},
  title        = {Phase transition to frequency entrainment in a long chain of pulse-coupled oscillators},
  url          = {http://dx.doi.org/10.1103/PhysRevE.66.016105},
  volume       = {66},
  year         = {2002},
}