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Extreme sensitivity to detuning for globally coupled phase oscillators
Peter Ashwin1, Oleksandr Burylko, Yuri Maistrenko
1Department of Mathematical Sciences, University of Exeter, Exeter EX4 4QE, United Kingdom.
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 > or = 5 oscillators.
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