Frequency adjustment and synchrony in networks of delayed pulse coupled oscillators

We introduce a system of pulse coupled oscillators that can change both their phases and frequencies; and prove that when there is a separation of time scales between phase and frequency adjustment the system converges to exact synchrony on strongly connected graphs with time delays. The analysis involves decomposing the network into a forest of tree-like structures that capture causality. Furthermore, we provide a lower bound for the size of the basin of attraction with immediate implications for empirical networks and random graph models. These results provide a robust method of sensor net synchronization as well as demonstrate a new avenue of possible pulse coupled oscillator research.