Recent theory showed that phase locking of two oscillators can occur only when the connector contributes zero or r phase change. Here we will present results on the phase locking of multiple oscillators. Two configurations are considered: (1) Centrally connected oscillators - peripheral units are not connected, but connected individually to a central unit; (2) Ring-connected oscillators - all units are connected in a ring configuration. The preliminary result is that the centrally connected oscillators phase lock better than the ring-connected oscillators. This is because it takes a longer time for all the oscillators to communicate to each other in the second case. Temporal behaviors were solved numerically, which found the phase locking depends strongly upon the connector lengths, the connecting ports and the modes of operation of the oscillators.
"Phase Locking Of Multiple Microwave Oscillators", Proc. SPIE 1061, Microwave and Particle Beam Sources and Directed Energy Concepts, (25 July 1989); doi: 10.1117/12.951800; https://doi.org/10.1117/12.951800