Exact analysis of spontaneous phase synchronization of two identical coupled electrical linear LC oscillators

This paper provides contributions to the study of phase synchronization transient two identical linear LC oscillators, coupled through a resistor. The main contribution is obtaining an exact equation that represents, as function time, evolution angle between from initial condition until synchronization. It demonstrated system has equilibrium points, one unstable when equal π, and other stable it zero which converges for any value than π. also dynamics oscillators can be described by Kuramoto model. An analysis energy dissipated during presented concept introduced. results theoretical are verified with use computer simulation.