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Synchronization of two LC-oscillators using nonlinear models

Synchronization of two LC-oscillators is a deeply nonlinear process. We consider synchronization of two van der Pol oscillators using different coupling circuits (four cases are considered), and coupled via first harmonic. We derive the equations for calculation of the synchronization frequency, and the equations for the oscillation amplitudes. It is shown that, in the general case, the synchronization frequency is different from the frequencies of individual oscillators before coupling. The oscillation amplitudes are also not equal: one oscillator becomes a master, and the other oscillator becomes a slave.