Phase transition to frequency entrainment in a long chain of pulsecoupled oscillators
(2002) In Physical Review E 66(1). Abstract
 A long chain of pulsecoupled 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 frequencyentrained 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 frequencyentrained oscillators emerged. The cluster sizes were exponentially distributed, even when the critical coupling was approached. At... (More)
 A long chain of pulsecoupled 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 frequencyentrained 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 frequencyentrained 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:
https://lup.lub.lu.se/record/331891
 author
 Östborn, Per ^{LU}
 organization
 publishing date
 2002
 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
 pmid:12241424
 ISSN
 1063651X
 DOI
 10.1103/PhysRevE.66.016105
 language
 English
 LU publication?
 yes
 id
 d172cee81245433e9be0370e821468a9 (old id 331891)
 date added to LUP
 20160401 16:29:05
 date last changed
 20201122 05:56:12
@article{d172cee81245433e9be0370e821468a9, abstract = {A long chain of pulsecoupled 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 frequencyentrained 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 frequencyentrained 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 = {1063651X}, language = {eng}, number = {1}, publisher = {American Physical Society}, series = {Physical Review E}, title = {Phase transition to frequency entrainment in a long chain of pulsecoupled oscillators}, url = {http://dx.doi.org/10.1103/PhysRevE.66.016105}, doi = {10.1103/PhysRevE.66.016105}, volume = {66}, year = {2002}, }