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Control of synchrony by delay coupling in complex networks
Using a master stability function approach, we study synchronization
in delay-coupled oscillator networks. The oscillators are modeled by a
complex normal form of super- or subcritical Hopf bifurcation. We derive
analytical stability conditions and demonstrate that by tuning the phase of
the complex coupling constant one can easily control the stability of synchronous
periodic states. The phase is identified as a crucial control parameter to
switch between in-phase synchronization or desynchronization for general network
topologies. For unidirectionally coupled rings or more general networks
described by circulant matrices the coupling phase controls in-phase, cluster,
or splay states. Our results are robust even for slightly nonidentical oscillators.