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Complete synchronization of Kuramoto oscillators

Kuramoto oscillator networks represent a standard model of synchronization analysis. Extensive studies have shown that static interactions can only bring about a partial synchronization (phase locking). This paper investigates the complete synchronization, where the oscillator outputs follow exactly a common trajectory. It is shown that oscillators with individual natural frequencies can be synchronized by dynamic couplings with integrator dynamics. A necessary and sufficient synchronization condition is derived, which shows that oscillators with positive parameters are completely synchronized for arbitrary coupling strength.