Dynamic edge adaptation in delayed oscillator networks

We consider edge dynamics for networks of non-identical time-delayed Kuramoto oscillators. The dynamics that we derive ensure synchronization to an arbitrary design frequency whilst minimizing the edge weights in the graph. The approach was inspired by inhibitory neurons in the brain and makes use of positive and negative coupling between oscillators. By using the dual of an optimization problem we obtain edge dynamics that are simple and decentralized. We present simulations to demonstrate our approach and investigate a network derived from the CoCoMac (Collations of Connectivity data on the Macaque brain) database.