Isochronicity-induced bifurcations in systems of weakly dissipative couples oscillators

We consider the dynamics of networks of oscillators that are weakly dissipative perturbations of identical Hamiltonian oscillators with weak coupling. If the coupling is much weaker than the dissipation we can use averaging to reduce the system to phase equations on a torus. We consider example applications to two and three weakly diffusively coupled oscillators with points of isochronicity and reduce to approximating flows on tori. We use this to identify bifurcation of various periodic solutions on perturbing away from a point of isochronicity.