oscillators have been used to model groups of fireflies [@Mirollo.90.SIAMJAM.BiologicalOscillators], spiking neurons [@Pikovsky.ea.03.BiologicalOscillators; @gerstner2002spiking], muscle cells [@Peskin.75.BiologicalOscillators], wireless networks [@hong2010cooperative], and sensor networks [@Liu05adynamic]. With synchronization being a property of particular interest, such complex networks have been found to coordinate the values of their state variables by sharing information only at the times the events/impulses occur [@Mirollo.90.SIAMJAM.BiologicalOscillators; @Abbott1993].

The opposite of synchronization is [*desynchronization*]{}. In simple words, desynchronization in multi-agent systems is the notion that the agents’ periodic actions are separated “as far apart” as possible in time. Desynchronization is similar to clustering or splay-state configurations, and is sometimes referred in the literature as inhibited behavior [@mauroy:037122; @glass1988clocks]. For impulse-coupled oscillators, desynchronization is given as the behavior in which the separation between all of the timers impulses is equal [@Patel.Desync2007]. This behavior has been found to be present in communication schemes in fish [@Benda.Neuron] and in networks of spiking neurons [@Pfurtscheller19991842; @1997Natur.390.70S]. Desynchronization of oscillators has recently been shown to be of importance in the understanding of Parkinson’s disease [@Mabi.Moehlis2010; @Majtanik.Dolan2004], in the design of algorithms that limit the amount of overlapping data transfer and data loss in wireless digital networks [@hong2010cooperative], and in the design of round-robin scheduling schemes 