Extreme Sensitivity to Detuning for Globally Coupled Phase Oscillators
University of Exeter; National Academy of Sciences of Ukraine; Institute of Medicine and Virtual Institute of Neuromodulation, Jülich, Germany
Physical Review Letters
American Physical Society
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 ≥ 5 oscillators.
Peter Ashwin, Oleksandr Burylko, Yuri Maistrenko, and Oleksandr Popovych, Physical Review Letters, Vol. 96, p. 054102 (2006). "Copyright © 2006 by the American Physical Society."
96, pp. 054102