Selecting the coupling variable to synchronize nonlinear oscillators

The choice of which state variable to use in coupling network oscillators is a critical factor to reach synchronization. Nonetheless, few works have developed procedures to aid in such a choice, and in many studies, the coupling variable is chosen in an ad hoc fashion without any justification. To avoid a such situation, in this work, a procedure based on the Master Stability Function (MSF) is developed to rank the state variables according to their coupling ability to reach a Complete Synchronization (CS) in networks of identical oscillators. In some cases, the only information needed is the oscillator dynamics, in other cases, the ranking of coupling variables also requires information about the network topology. The developed criteria are related to features such as coupling strength and the speed with which disturbances are rejected. The results are validated via Monte Carlo simulation of the networks.