Analysis and Design of Phase Desynchronization in Pulse-coupled Oscillators

By spreading phases on the unit circle, desynchronization algorithm is a powerful tool to achieve round-robin scheduling, which is crucial in applications as diverse as media access control of communication networks, realization of analog-to-digital converters, and scheduling of traffic flows in intersections. Driven by the increased application of pulse-coupled oscillators in achieving synchronization, desynchronization of pulse-coupled oscillators is also receiving more attention. In this paper, we propose a phase desynchronization algorithm by rigorously analyzing the dynamics of pulse-coupled oscillators and carefully designing the pulse based interaction function. A systematic proof for convergence to phase desynchronization is also given. Different from many existing results which can only achieve equal separation of firing time instants, the proposed approach can achieve equal separation of phases, which is more difficult to achieve due to phase jumps in pulse-coupled oscillators. Furthermore, the new strategy can guarantee achievement of desynchronization even when some nodes have identical initial phases, a situation which fails most existing desynchronization approaches. Numerical simulation results are provided to illustrate the effectiveness of the theoretical results.