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Frequency entrainment in long chains of oscillators with random natural frequencies in the weak coupling limit

Östborn, Per LU (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)
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author
organization
publishing date
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
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
2007-10-29 12:35:24
date last changed
2017-01-01 07:11:07
@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},
  volume       = {70},
  year         = {2004},
}