Discrete time Kuramoto models with delay

Motivated by the needs of multiagent systems in the presence of sensing and communication that is delayed, intermittent and asynchronous, we present here a discrete-time Kuramoto oscillator model that incorporates delays. Analytical results are derived for certain cases of heading-based stability of synchronized and balanced equilibrium sets both when delay is not present and when it is. In all cases, agents are assumed to be identical and fully connected, with constant and equal network delays. For complex cases, the analysis is supplemented with Monte Carlo simulations, and all results are demonstrated in simulation.