The paper is concermed with the array of identical coupled oscillators with delay
where is considered mod , , , and . The system is -equivariant and has an equilibrium at the origin.
The author studies stability of the origin and properties of the bifurcating solutions. In particular, the analysis of the characteristic equation reveals multiple Hopf (or pitchfork) bifurcations, which give rise to a variety of symmetric periodic solutions (or equilibria) as the delay or another bifurcation parameter varies.