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

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