We study the synchronization of coupled identical circulant and non-circulant oscillators using single variable and different multi-variable coupling schemes. We use the master stability function to determine conditions for synchronization, in particular the necessary coupling parameter that ensures a stable synchronization manifold.

We show that for circulant oscillators, the smallest coupling parameter for synchronization is needed when multi-variable coupling with the same coupling coefficients is applied. Conversely, for non-circulant oscillators, no such general conclusions are attainable in that the smallest coupling parameter cannot be attributed to a particular coupling setup.