# Avalanches impede synchronization of jammed oscillators

## TL;DR

This paper introduces a generalized oscillator model with phase repulsion, revealing that avalanches and desynchronization emerge at intermediate repulsion levels, resembling real-world cascade phenomena like neuronal avalanches.

## Contribution

It presents an analytically solvable model showing how short-range phase repulsion induces avalanches and desynchronization, linking critical dynamics to oscillator heterogeneity and mutual repulsion.

## Key findings

- Avalanches occur at intermediate repulsion strengths.
- The model's avalanche statistics resemble neuronal avalanches.
- Analytical relations connect heterogeneity and repulsion to system dynamics.

## Abstract

Synchrony is inevitable in many oscillating systems -- from the canonical alignment of two ticking grandfather clocks, to the mutual entrainment of beating flagella or spiking neurons. Yet both biological and manmade systems provide striking examples of spontaneous desynchronization, such as failure cascades in alternating current power grids or neuronal avalanches in the mammalian brain. Here, we generalize classical models of synchronization among heterogenous oscillators to include short-range phase repulsion among individuals, a property that abets the emergence of a stable desynchronized state. Surprisingly, we find that our model exhibits self-organized avalanches at intermediate values of the repulsion strength, and that these avalanches have similar statistical properties to cascades seen in real-world systems such as neuronal avalanches. We find that these avalanches arise due to a critical mechanism based on competition between mean field recruitment and local displacement, a property that we replicate in a classical cellular automaton model of traffic jams. We exactly solve our system in the many-oscillator limit, and obtain analytical results relating the onset of avalanches or partial synchrony to the relative heterogeneity of the oscillators, and their degree of mutual repulsion. Our results provide a minimal analytically-tractable example of complex dynamics in a driven critical system.