Frequency entrainment in long chains of oscillators with random natural frequencies in the weak coupling limit
(2004) In Physical Review E 70(1).- Abstract
- We study oscillator chains of the form phi(k)=omega(k)+K[Gamma(phi(k-1)-phi(k))+Gamma(phi(k+1)-phi(k))], where phi(k)is an element of[0,2pi) is the phase of oscillator k. In the thermodynamic limit where the number of oscillators goes to infinity, for suitable choices of Gamma(x), we prove that there is a critical coupling strength K-c, above which a stable frequency-entrained state exists, but below which the probability is zero to have such a state. It is assumed that the natural frequencies are random with finite bandwidth. A crucial condition on Gamma(x) is that it is nonodd, i.e.,Gamma(x)+Gamma(-x)not equal0. The interest in the results comes from the fact that any chain of limit-cycle oscillators can be described by equations of the... (More)
- We study oscillator chains of the form phi(k)=omega(k)+K[Gamma(phi(k-1)-phi(k))+Gamma(phi(k+1)-phi(k))], where phi(k)is an element of[0,2pi) is the phase of oscillator k. In the thermodynamic limit where the number of oscillators goes to infinity, for suitable choices of Gamma(x), we prove that there is a critical coupling strength K-c, above which a stable frequency-entrained state exists, but below which the probability is zero to have such a state. It is assumed that the natural frequencies are random with finite bandwidth. A crucial condition on Gamma(x) is that it is nonodd, i.e.,Gamma(x)+Gamma(-x)not equal0. The interest in the results comes from the fact that any chain of limit-cycle oscillators can be described by equations of the above form in the limits of weak coupling and narrow distribution of natural frequencies. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/271084
- author
- Östborn, Per LU
- organization
- publishing date
- 2004
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Physical Review E
- volume
- 70
- issue
- 1
- publisher
- American Physical Society
- external identifiers
-
- wos:000223135800033
- scopus:37649029744
- pmid:15324142
- ISSN
- 1063-651X
- DOI
- 10.1103/PhysRevE.70.016120
- language
- English
- LU publication?
- yes
- id
- 1c81b6db-ce21-4078-83ca-f0c7be1f6e79 (old id 271084)
- date added to LUP
- 2016-04-01 16:39:07
- date last changed
- 2022-01-28 21:12:11
@article{1c81b6db-ce21-4078-83ca-f0c7be1f6e79,
abstract = {{We study oscillator chains of the form phi(k)=omega(k)+K[Gamma(phi(k-1)-phi(k))+Gamma(phi(k+1)-phi(k))], where phi(k)is an element of[0,2pi) is the phase of oscillator k. In the thermodynamic limit where the number of oscillators goes to infinity, for suitable choices of Gamma(x), we prove that there is a critical coupling strength K-c, above which a stable frequency-entrained state exists, but below which the probability is zero to have such a state. It is assumed that the natural frequencies are random with finite bandwidth. A crucial condition on Gamma(x) is that it is nonodd, i.e.,Gamma(x)+Gamma(-x)not equal0. The interest in the results comes from the fact that any chain of limit-cycle oscillators can be described by equations of the above form in the limits of weak coupling and narrow distribution of natural frequencies.}},
author = {{Östborn, Per}},
issn = {{1063-651X}},
language = {{eng}},
number = {{1}},
publisher = {{American Physical Society}},
series = {{Physical Review E}},
title = {{Frequency entrainment in long chains of oscillators with random natural frequencies in the weak coupling limit}},
url = {{http://dx.doi.org/10.1103/PhysRevE.70.016120}},
doi = {{10.1103/PhysRevE.70.016120}},
volume = {{70}},
year = {{2004}},
}