Synchronization of oscillators not sharing a common ground

Networks of coupled LC oscillators that do not share a common ground node are studied. Both resistive coupling and inductive considered. For networks under coupling, it is shown the oscillator-coupler interconnection has to be bilayer if oscillator voltages asymptotically synchronize. Also, for architecture (when both couplers present) method proposed compute complex-valued effective Laplacian matrix represents overall coupling. It proved display synchronous behavior only single eigenvalue on imaginary axis.