  Synchrony of neuronal ensembles is believed to facilitate information
exchange among cortical regions in the human brain. Recently, it has been
observed that distant brain areas which are not directly connected by neural
links also experience synchronization. Such synchronization between remote
regions is sometimes due to the presence of a mediating region connecting them,
e.g., \textit{the thalamus}. The underlying network structure of this
phenomenon is star-like and motivates us to study the \textit{remote
synchronization} of Kuramoto oscillators, {modeling neural dynamics}, coupled
by a directed star network, for which peripheral oscillators get phase
synchronized, remaining the accommodating central mediator at a different
phase. We show that the symmetry of the coupling strengths of the outgoing
links from the central oscillator plays a crucial role in enabling stable
remote synchronization. We also consider the case when there is a phase shift
in the model which results from synaptic and conduction delays. Sufficient
conditions on the coupling strengths are obtained to ensure the stability of
remotely synchronized states. To validate our obtained results, numerical
simulations are also performed.
