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Self-organized quasi periodicity is one of the most puzzling dynamical phasesobserved in systems of non linear coupled oscillators. The single dynamicalunits are not locked to the periodic mean field they produce, but they stillfeature a coherent behavior, through an unexplained complex form ofcorrelation. We consider a class of leaky integrate-and-fire oscillators onrandom sparse and massive networks with dynamical synapses, featuringself-organized quasi periodicity, and we show how complex collectiveoscillations arise from constructive interference of microscopic dynamics. Inparticular, we find a simple quantitative relationship between two relevantmicroscopic dynamical time scales and the macroscopic time scale of the globalsignal. We show that the proposed relation is a general property of collectiveoscillations, common to all the partially synchronous dynamical phasesanalyzed. We argue that an analogous mechanism could be at the origin ofsimilar network dynamics.

A microscopic mechanism for self-organized quasi periodicity in random networks of non linear oscillators