Ponies on a merry-go-round in large arrays of Josephson junctions

Numerical simulation of periodic solutions in large arrays of Josephson junctions indicates the existence of periodic solutions where each junction oscillates with the same waveform, but with equal phase lags. These solutions are called ponies on a merry-go-round or POMs for short. The authors prove the existence of POMs in the equations modelling large arrays of Josephson junctions by using global bifurcation techniques. The basic idea is to view the period of the solution and the phase lag as independent parameters and to prove, using a priori estimates, that the synchronous solution (with phase lag set to zero) can be continued to a solution with phase lag equal to (1/N)th of the period, a POM.