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Linear stability of synchronized states in networks of delay-coupledoscillators depends on the type of interaction, the network and oscillatorproperties. For inert oscillator response, found ubiquitously from biology toengineering, states with time-dependent frequencies can arise. These generateside bands in the frequency spectrum or lead to chaotic dynamics. Stabilityanalysis is difficult due to delay-induced multistability and has only beenavailable via numerical approaches. We derive criteria and conditions thatenable fast and robust analytical linear stability analysis based on the systemparameters. These apply to arbitrary network topologies, identical oscillatorsand delays.

Synchronization in the presence of time delays and inertia: Stability criteria