Reentrant synchronization and pattern formation in pacemaker-entrained Kuramoto oscillators
Radicchi, F,, Meyer-Ortmanns, HPhys. Rev. E 74, 026203 (2006)
Times cited: 8
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.