Synchronization of Phase-coupled Oscillators with Arbitrary Topology

This paper studies networks of identical phase-coupled oscillators with arbitrary underlying connected graph. By using results from algebraic graph theory, a sufficient condition is obtained which can be used to check equilibrium stability. This condition generalizes existing results and can solve some previously unsolved cases. It also leads to the first sufficient condition on the coupling function with which the system is guaranteed to reach synchronization. Through out the paper, several examples are used to verify and illustrate the theory. We also correct some mistakes in the existing literature.