# Competitive Suppression of Synchronization and Non-Monotonic Transitions in Oscillator Communities with Distributed Time Delay

## TL;DR

This paper investigates how community structure and distributed time delays in coupled oscillators lead to complex, non-monotonic synchronization transitions, including asymmetric suppression and competition among communities.

## Contribution

It introduces a detailed analysis of the combined effects of community structure and time delays on synchronization, revealing non-monotonic and asymmetric transition phenomena.

## Key findings

- Increasing coupling can both promote and inhibit synchronization.
- Asymmetric suppression occurs where communities compete to dominate synchronization.
- Analytical descriptions confirm numerical simulation results.

## Abstract

Community structure and interaction delays are common features of ensembles of network coupled oscillators, but their combined effect on the emergence of synchronization has not been studied in detail. We study the transitions between macroscopic states in coupled oscillator systems with community structure and time delays. We show that the combination of these two properties gives rise to non-monotonic transitions, whereby increasing the global coupling strength can both inhibit and promote synchronization, yielding both desynchronization and synchronization transitions. For relatively wide parameter choices we also observe asymmetric suppression of synchronization, where communities compete to suppress one another's synchronization properties until one or more win, totally suppressing the others to effective incoherence. Using the ansatz of Ott and Antonsen we provide analytical descriptions for these transitions that confirm numerical simulations.