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Reentrant synchronization and pattern formation in pacemaker-entrained Kuramoto oscillators.

Authors
Type
Published Article
Journal
Physical review. E, Statistical, nonlinear, and soft matter physics
Publication Date
Volume
74
Issue
2 Pt 2
Pages
26203–26203
Identifiers
PMID: 17025521
Source
Medline
License
Unknown

Abstract

We study phase entrainment of Kuramoto oscillators under different conditions on the interaction range and the natural frequencies. In the first part the oscillators are entrained by a pacemaker acting like an impurity or a defect. We analytically derive the entrainment frequency for arbitrary interaction range and the entrainment threshold for all-to-all couplings. For intermediate couplings our numerical results show a reentrance of the synchronization transition as a function of the coupling range. The origin of this reentrance can be traced back to the normalization of the coupling strength. In the second part we consider a system of oscillators with an initial gradient in their natural frequencies, extended over a one-dimensional chain or a two-dimensional lattice. Here it is the oscillator with the highest natural frequency that becomes the pacemaker of the ensemble, sending out circular waves in oscillator-phase space. No asymmetric coupling between the oscillators is needed for this dynamical induction of the pacemaker property nor need it be distinguished by a gap in the natural frequency.

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