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(k1)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 Kc, above which a stable frequencyentrained 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 limitcycle oscillators can be described by equations of the... (More)
 We study oscillator chains of the form phi(k)=omega(k)+K[Gamma(phi(k1)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 Kc, above which a stable frequencyentrained 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 limitcycle 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:
http://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
 ISSN
 1063651X
 DOI
 10.1103/PhysRevE.70.016120
 language
 English
 LU publication?
 yes
 id
 1c81b6dbce21407883caf0c7be1f6e79 (old id 271084)
 date added to LUP
 20071029 12:35:24
 date last changed
 20190220 08:07:33
@article{1c81b6dbce21407883caf0c7be1f6e79, abstract = {We study oscillator chains of the form phi(k)=omega(k)+K[Gamma(phi(k1)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 Kc, above which a stable frequencyentrained 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 limitcycle 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 = {1063651X}, 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}, }