Some properties of two series-connected synchronized van der Pol oscillators

The theory of synchronized oscillators which obey the van der Pol equation is extended to include the case of two series-connected oscillators, i.e., a situation where the phases of the oscillations are subject to constraint. A solution is found for the case of identical oscillators, and a perturbation method is used to find the modification required when the oscillators are not identical. Experimental results presented for an interesting special case show good agreement with theory in the range over which the perturbation theory can be expected to be valid.