  Linear stability of synchronized states in networks of delay-coupled
oscillators depends on the type of interaction, the network and oscillator
properties. For inert oscillator response, found ubiquitously from biology to
engineering, states with time-dependent frequencies can arise. These generate
side bands in the frequency spectrum or lead to chaotic dynamics. Stability
analysis is difficult due to delay-induced multistability and has only been
available via numerical approaches. We derive criteria and conditions that
enable fast and robust analytical linear stability analysis based on the system
parameters. These apply to arbitrary network topologies, identical oscillators
and delays.
