  We study the coupling induced destabilization in an array of identical
oscillators coupled in a ring structure where the number of oscillators in the
ring is large. The coupling structure includes different types of interactions
with several next neighbors. We derive an amplitude equation of Ginzburg-Landau
type, which describes the destabilization of a uniform stationary state in a
ring with a large number of nodes. Applying these results to unidirectionally
coupled Duffing oscillators, we explain the phenomenon of a fast transition to
chaos, which has been numerically observed in such systems. More specifically,
the transition to chaos occurs on an interval of a generic control parameter
that scales as the inverse square of the size of the ring, i.e. for
sufficiently large system, we observe practically an immediate transition to
chaos.
