D. Aronson, M. Golubitsky and J. Mallet-Paret
Ponies on a merry-go-round in large arrays of Josephson junctions
Nonlinearity. 4 (1991) 903-910.
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. In this
paper we prove the existence of POMs in the equations modelling large arrays
of Josephson junctions by using global bifurcation techiques. 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.