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

TL;DR

This paper develops analytical criteria for assessing the linear stability of synchronized states in delay-coupled oscillator networks with inertia, accounting for complex dynamics like frequency side bands and chaos.

Contribution

It introduces universal stability criteria applicable to arbitrary network topologies, oscillators, and delays, simplifying analysis of delay-induced multistability and complex dynamics.

Findings

Derived analytical stability conditions for delay-coupled oscillators with inertia.

Applicable to arbitrary network structures and identical oscillators.

Facilitates fast stability assessment without extensive numerical simulations.

Abstract

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.