Synchronization of Pulse-Coupled Oscillators and Clocks under Minimal Connectivity Assumptions
Provides a more general mathematical foundation for clock synchronization in wireless sensor networks with minimal connectivity assumptions.
The paper extends synchronization results for pulse-coupled oscillators from strongly connected networks to networks with a directed spanning tree, proving this condition is both sufficient and necessary.
Populations of flashing fireflies, claps of applauding audience, cells of cardiac and circadian pacemakers reach synchrony via event-triggered interactions, referred to as pulse couplings. Synchronization via pulse coupling is widely used in wireless sensor networks, providing clock synchronization with parsimonious packet exchanges. In spite of serious attention paid to networks of pulse coupled oscillators, there is a lack of mathematical results, addressing networks with general communication topologies and general phase-response curves of the oscillators. The most general results of this type (Wang et al., 2012, 2015) establish synchronization of oscillators with a delay-advance phase-response curve over strongly connected networks. In this paper we extend this result by relaxing the connectivity condition to the existence of a root node (or a directed spanning tree) in the graph. This condition is also necessary for synchronization.