Synchronization of Kuramoto model with anticipatory agents

This thesis investigates a system of coupled Kuramoto oscillators on undirected networks comprising of anticipatory agents that try to predict the future states of their neighbors and adjust their states accordingly. The prediction is done using the past behavior of the neighbors and leads to a set of coupled delay differential equations. The study reveals that the anticipatory behavior leads to the emergence of multiple phase-synchronized solutions characterized by distinct collective frequencies and stability properties. An exact criterion for the stability of the phase-synchronized states is derived. It is shown that the system can exhibit multi-stability, where different phase-synchronized solutions can be observed depending on the initial conditions. It is further proved that bipartite graphs can exhibit anti-phase solutions and an exact condition for their stability is provided. Investigation of cycle graphs yields further frequency-synchronized states, in various clustered patterns, depending on the system’s parameter values.