Entrainment of coupled oscillators on regular networks by pacemakers
Radicchi, F, Meyer-Ortmanns, HPhys. Rev. E 73, 036218 (2006)
Times cited: 17
Abstract
We study Kuramoto oscillators, driven by one pacemaker, on
d-dimensional regular topologies with nearest neighbor interactions. We
derive the analytical expressions for the common frequency in the case
of phase-locked motion and for the critical frequency of the pacemaker,
placed at an arbitrary position in the lattice, so that above the
critical frequency no phase-locked motion is possible. We show that the
mere change in topology from an open chain to a ring induces
synchronization for a certain range of pacemaker frequencies and
couplings, while keeping the other parameters fixed. Moreover, we
demonstrate numerically that the critical frequency of the pacemaker
decreases as a power of the linear size of the lattice with an exponent
equal to the dimension of the system. This leads in particular to the
conclusion that for infinite-dimensional topologies the critical
frequency for having entrainment decreases exponentially with
increasing size of the system, or, more generally, with increasing
depth of the network, that is, the average distance of the oscillators
from the pacemaker.