  The property of desynchronization in an all-to-all network of homogeneous
impulse-coupled oscillators is studied. Each impulse-coupled oscillator is
modeled as a hybrid system with a single timer state that self-resets to zero
when it reaches a threshold, at which event all other impulse-coupled
oscillators adjust their timers following a common reset law. In this setting,
desynchronization is considered as each impulse-coupled oscillator's timer
having equal separation between successive resets. We show that, for the
considered model, desynchronization is an asymptotically stable property. For
this purpose, we recast desynchronization as a set stabilization problem and
employ Lyapunov stability tools for hybrid systems. Furthermore, several
perturbations are considered showing that desynchronization is a robust
property. Perturbations on both the continuous and discrete dynamics are
considered. Numerical results are presented to illustrate the main
contributions.
