Synchronization in Networks of Anticipatory Agents

We consider a coupled Kuramoto system composed of agents that anticipate the future states of their neighbors based on past data and try to align their states accordingly. We show that this anticipatory behavior results in multiple synchronized solutions at different collective frequencies and different stability characteristics. We derive an exact condition for the stability of the synchronized states. We show that the system can exhibit multistability, converging to different synchronized solutions depending on the initial conditions.