2020/05/09 by S. Emre Tuna, Tuna, S. Emre
Computer Science · Engineering · #Dynamical Systems (math.DS) #FOS: Mathematics #Molecular Junctions and Nanostructures #Nonlinear Dynamics and Pattern Formation #Semiconductor Lasers and Optical Devices
paper · pdf · doi:10.48550/arxiv.2005.04403
openalex publication_date 2020/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Networks of coupled LC oscillators that do not share a common ground node are studied. Both resistive coupling and inductive coupling are considered. For networks under resistive coupling, it is shown that the oscillator-coupler interconnection has to be bilayer if the oscillator voltages are to asymptotically synchronize. Also, for bilayer architecture (when both resistive and inductive couplers are present) a method is proposed to compute a complex-valued effective Laplacian matrix that represents the overall coupling. It is proved that the oscillators display synchronous behavior if and only if the effective Laplacian has a single eigenvalue on the imaginary axis.