We discuss the sensitivity of a population of coupled oscillators to differences in their natural frequencies, i.e., to detuning. We argue that for three or more oscillators, one can get great sensitivity even if the coupling is strong. For N globally coupled phase oscillators we find there can be bifurcation to extreme sensitivity, where frequency locking can be destroyed by arbitrarily small detuning. This extreme sensitivity is absent for N=2, appears at isolated parameter values for N=3 and N=4, and can appear robustly for open sets of parameter values for N>=5 oscillators.
%0 Journal Article
%1 ASH06
%A Ashwin, Peter
%A Burylko, Oleksandr
%A Maistrenko, Y.
%A Popovych, O. V.
%D 2006
%J Phys.~Rev.~Lett.
%K bifurcation; dynamical locked nonlinear oscillators; phase systems
%N 5
%P 054102
%R 10.1103/physrevlett.96.054102
%T Extreme Sensitivity to Detuning for Globally Coupled Phase Oscillators
%V 96
%X We discuss the sensitivity of a population of coupled oscillators to differences in their natural frequencies, i.e., to detuning. We argue that for three or more oscillators, one can get great sensitivity even if the coupling is strong. For N globally coupled phase oscillators we find there can be bifurcation to extreme sensitivity, where frequency locking can be destroyed by arbitrarily small detuning. This extreme sensitivity is absent for N=2, appears at isolated parameter values for N=3 and N=4, and can appear robustly for open sets of parameter values for N>=5 oscillators.
@article{ASH06,
abstract = {We discuss the sensitivity of a population of coupled oscillators to differences in their natural frequencies, i.e., to detuning. We argue that for three or more oscillators, one can get great sensitivity even if the coupling is strong. For N globally coupled phase oscillators we find there can be bifurcation to extreme sensitivity, where frequency locking can be destroyed by arbitrarily small detuning. This extreme sensitivity is absent for N=2, appears at isolated parameter values for N=3 and N=4, and can appear robustly for open sets of parameter values for N>=5 oscillators.},
added-at = {2009-03-03T17:19:04.000+0100},
author = {Ashwin, Peter and Burylko, Oleksandr and Maistrenko, Y. and Popovych, O. V.},
biburl = {https://www.bibsonomy.org/bibtex/2c0083e5038deb420709c8bcee8051cb3/bronckobuster},
doi = {10.1103/physrevlett.96.054102},
eid = {054102},
interhash = {378bd099196bc95caf4953712c980d99},
intrahash = {c0083e5038deb420709c8bcee8051cb3},
journal = {Phys.~Rev.~Lett.},
keywords = {bifurcation; dynamical locked nonlinear oscillators; phase systems},
number = 5,
numpages = {4},
pages = 054102,
timestamp = {2009-03-03T17:20:19.000+0100},
title = {Extreme Sensitivity to Detuning for Globally Coupled Phase Oscillators},
volume = 96,
year = 2006
}