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Wave patterns in frequency-entrained oscillator lattices

Strang, J E and Östborn, Per LU (2005) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00 72(5).
Abstract
We study and classify firing waves in two-dimensional oscillator lattices. To do so, we simulate a pulse-coupled oscillator model aimed to resemble a group of pacemaker cells in the heart. The oscillators are assigned random natural frequencies, and we focus on frequency entrained states. Depending on the initial condition, three types of wave landscapes are seen asymptotically. A concentric landscape contains concentric waves with one or more foci. Spiral landscapes contain one or more spiral waves. A mixed landscape contains both concentric and spiral waves. Mixed landscapes are only seen for moderate coupling strengths g, since for higher g, spiral waves have higher frequency than concentric waves, so that they cannot mix in frequency... (More)
We study and classify firing waves in two-dimensional oscillator lattices. To do so, we simulate a pulse-coupled oscillator model aimed to resemble a group of pacemaker cells in the heart. The oscillators are assigned random natural frequencies, and we focus on frequency entrained states. Depending on the initial condition, three types of wave landscapes are seen asymptotically. A concentric landscape contains concentric waves with one or more foci. Spiral landscapes contain one or more spiral waves. A mixed landscape contains both concentric and spiral waves. Mixed landscapes are only seen for moderate coupling strengths g, since for higher g, spiral waves have higher frequency than concentric waves, so that they cannot mix in frequency entrained states. If the initial condition is random, the probability to get a concentric landscape increases with increasing coupling strength g, but decreases with increasing lattice size. The g dependence of the probability enables hysteresis, where the system jumps between the two landscape types as g is continuously changed. For moderate g, spiral tips rotate around a suppressed oscillator that never fires. We call such an oscillator an oscillator defect. A spiral may also rotate around a point defect situated between the oscillators. In that case all oscillators fire at the entrained frequency. For larger g, a spiral tip either moves around a row of suppressed oscillators, a row defect, or around an open curve situated between the oscillators, which may be called a line defect. The length of a row or line defect increases with g. Our results may help understand sinus node reentry, where the natural pacemaker of the heart suddenly shifts to a higher frequency. Some of the observed phenomena seem generic, based on simulations of other models. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00
volume
72
issue
5
publisher
American Physical Society
external identifiers
  • wos:000233603200046
  • scopus:28844440454
ISSN
1539-3755
DOI
10.1103/PhysRevE.72.056137
language
English
LU publication?
yes
id
ae630a8c-3b79-4c4a-8d51-4d6e67b24575 (old id 211390)
date added to LUP
2007-10-05 15:39:15
date last changed
2017-08-20 03:28:16
@article{ae630a8c-3b79-4c4a-8d51-4d6e67b24575,
  abstract     = {We study and classify firing waves in two-dimensional oscillator lattices. To do so, we simulate a pulse-coupled oscillator model aimed to resemble a group of pacemaker cells in the heart. The oscillators are assigned random natural frequencies, and we focus on frequency entrained states. Depending on the initial condition, three types of wave landscapes are seen asymptotically. A concentric landscape contains concentric waves with one or more foci. Spiral landscapes contain one or more spiral waves. A mixed landscape contains both concentric and spiral waves. Mixed landscapes are only seen for moderate coupling strengths g, since for higher g, spiral waves have higher frequency than concentric waves, so that they cannot mix in frequency entrained states. If the initial condition is random, the probability to get a concentric landscape increases with increasing coupling strength g, but decreases with increasing lattice size. The g dependence of the probability enables hysteresis, where the system jumps between the two landscape types as g is continuously changed. For moderate g, spiral tips rotate around a suppressed oscillator that never fires. We call such an oscillator an oscillator defect. A spiral may also rotate around a point defect situated between the oscillators. In that case all oscillators fire at the entrained frequency. For larger g, a spiral tip either moves around a row of suppressed oscillators, a row defect, or around an open curve situated between the oscillators, which may be called a line defect. The length of a row or line defect increases with g. Our results may help understand sinus node reentry, where the natural pacemaker of the heart suddenly shifts to a higher frequency. Some of the observed phenomena seem generic, based on simulations of other models.},
  author       = {Strang, J E and Östborn, Per},
  issn         = {1539-3755},
  language     = {eng},
  number       = {5},
  publisher    = {American Physical Society},
  series       = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00},
  title        = {Wave patterns in frequency-entrained oscillator lattices},
  url          = {http://dx.doi.org/10.1103/PhysRevE.72.056137},
  volume       = {72},
  year         = {2005},
}