Wave patterns in frequencyentrained oscillator lattices
(2005) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)20010101+01:0020160101+01:00 72(5). Abstract
 We study and classify firing waves in twodimensional oscillator lattices. To do so, we simulate a pulsecoupled 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 twodimensional oscillator lattices. To do so, we simulate a pulsecoupled 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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/211390
 author
 Strang, J E and Östborn, Per ^{LU}
 organization
 publishing date
 2005
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)20010101+01:0020160101+01:00
 volume
 72
 issue
 5
 publisher
 American Physical Society
 external identifiers

 wos:000233603200046
 scopus:28844440454
 ISSN
 15393755
 DOI
 10.1103/PhysRevE.72.056137
 language
 English
 LU publication?
 yes
 id
 ae630a8c3b794c4a8d514d6e67b24575 (old id 211390)
 date added to LUP
 20071005 15:39:15
 date last changed
 20180107 05:07:23
@article{ae630a8c3b794c4a8d514d6e67b24575, abstract = {We study and classify firing waves in twodimensional oscillator lattices. To do so, we simulate a pulsecoupled 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 = {15393755}, language = {eng}, number = {5}, publisher = {American Physical Society}, series = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)20010101+01:0020160101+01:00}, title = {Wave patterns in frequencyentrained oscillator lattices}, url = {http://dx.doi.org/10.1103/PhysRevE.72.056137}, volume = {72}, year = {2005}, }