In this talk, I will describe the dynamics of a system of sinusoidally coupled phase oscillators on cubic graphs. The synchronous solution is always an attractor. However, as the graphs get larger (more nodes), it is possible to get other stable attractors. We study the basins, energy, and degree of stability of these non-synchronous attractors for all cubic graphs up to a certain number of nodes. We also use some techniques from computational algebraic geometry to show that for some graphs, the only attractor is synchrony.