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

Amplitude equations and fast transition to chaos in rings of coupled oscillators