Synchronization in Oscillator Networks: Switching Topologies and Non-homogeneous Delays

We investigate the problem of synchronization in oscillator networks when the delay inherent in such systems is taken into account. We first investigate a general Kuramoto- type model with heterogeneous time delays, both with a complete network as well as a nearest neighbor interaction, for which we propose conditions for synchronization around a rotating frequency. Then, we turn our attention to the problem of synchronization when the topologies are allowed to change. We show that synchronization is possible in the presence of delay, using a common Lyapunov functional argument.