Convergence of Self-Organizing Pulse-Coupled Oscillator Synchronization in Dynamic Networks

The theory of pulse-coupled oscillators provides a framework to formulate and develop self-organizing synchronization strategies for wireless communications and mobile computing. These strategies show low complexity and are adaptive to changes in the network. Even though several protocols have been proposed and theoretical insight was gained there is no proof that guarantees synchronization of the oscillator phases in general dynamic coupling topologies under technological constraints. Here, we introduce a family of coupling strategies for pulse-coupled oscillators and prove that synchronization emerges for systems with arbitrary connected and dynamic topologies, individually changing signal propagation and processing delays, and stochastic pulse emission. It is shown by simulations how unreliable links or intentionally incomplete communication between oscillators can improve synchronization performance.