Wave patterns in frequency-entrained oscillator lattices
(2005) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 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)
Please use this url to cite or link to this publication:
https://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)
- volume
- 72
- issue
- 5
- publisher
- American Physical Society
- external identifiers
-
- wos:000233603200046
- scopus:28844440454
- pmid:16383718
- ISSN
- 1539-3755
- DOI
- 10.1103/PhysRevE.72.056137
- language
- English
- LU publication?
- yes
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Mathematical Physics (Faculty of Technology) (011040002), Classical archaeology and ancient history (015004001)
- id
- ae630a8c-3b79-4c4a-8d51-4d6e67b24575 (old id 211390)
- date added to LUP
- 2016-04-01 11:35:34
- date last changed
- 2022-01-26 07:20:46
@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)}},
title = {{Wave patterns in frequency-entrained oscillator lattices}},
url = {{http://dx.doi.org/10.1103/PhysRevE.72.056137}},
doi = {{10.1103/PhysRevE.72.056137}},
volume = {{72}},
year = {{2005}},
}