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

TL;DR

This paper uncovers a microscopic mechanism explaining self-organized quasi periodicity in networks of non-linear oscillators, revealing how microscopic dynamics produce complex collective oscillations.

Contribution

It introduces a quantitative relationship linking microscopic time scales to macroscopic oscillations in networks of leaky integrate-and-fire oscillators.

Findings

Constructive interference of microscopic dynamics causes collective oscillations.

A simple relation between microscopic and macroscopic time scales is established.

The mechanism is general across various partially synchronous phases.

Abstract

Self-organized quasi periodicity is one of the most puzzling dynamical phases observed in systems of non linear coupled oscillators. The single dynamical units are not locked to the periodic mean field they produce, but they still feature a coherent behavior, through an unexplained complex form of correlation. We consider a class of leaky integrate-and-fire oscillators on random sparse and massive networks with dynamical synapses, featuring self-organized quasi periodicity, and we show how complex collective oscillations arise from constructive interference of microscopic dynamics. In particular, we find a simple quantitative relationship between two relevant microscopic dynamical time scales and the macroscopic time scale of the global signal. We show that the proposed relation is a general property of collective oscillations, common to all the partially synchronous dynamical phases analyzed. We argue that an analogous mechanism could be at the origin of similar network dynamics.