  We study the destabilization mechanism in a unidirectional ring of identical
oscillators, perturbed by the introduction of a long-range connection. It is
known that for a homogeneous, unidirectional ring of identical Stuart-Landau
oscillators the trivial equilibrium undergoes a sequence of Hopf bifurcations
eventually leading to the coexistence of multiple stable periodic states
resembling the Eckhaus scenario. We show that this destabilization scenario
persists under small non-local perturbations. In this case, the Eckhaus line is
modulated according to certain resonance conditions. In the case when the
shortcut is strong, we show that the coexisting periodic solutions split up
into two groups. The first group consists of orbits which are unstable for all
parameter values, while the other one shows the classical Eckhaus behavior.
