Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling

We consider a ring of identical elements with time delayed, nearest-neighbour coupling. The individual elements are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. The bifurcation and stability of nontrivial asynchronous oscillations from the trivial solution are analysed using equivariant bifurcation theory and centre manifold construction.