Synchronization phenomena in many oscillators coupled by resistors as a ring

In this article, we investigate the synchronization phenomena in N oscillators coupled by resistors as a ring. Since the system tends to minimize the energy consumed by the coupling resistors, the phase shift must be ±π and ±(N-1)π/N, for the case of N is even and odd respectively. In addition, only for the case of N is odd, we confirmed that the oscillation was stopped in some range of the coupling resistors. It is interesting that this phenomenon occurs for parameter values which are not too large or too small. These interesting phenomena are confirmed by both of circuit experiments and numerical calculations, and are analyzed by the averaging method theoretically