  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.
