This paper considers a system of identical parametric oscillators linearly
coupled together in a ring geometry. The phase of the coupling is chosen so
that the system takes on steady, rather than oscillatory, states, and this
work focuses on the sequence of bifurcations from the zero steady state. C
enter manifold expressions are given for the forms of the solutions that em
erge from these bifurcations, and full expressions are given for special ca
ses. Secondary bifurcations are also briefly discussed.