Dynamics of unidirectionally coupled Duffing oscillators

We investigate the dynamics of a ring of unidirectionally coupled autonomous Duffing oscillators. Starting from a situation where the individual oscillator without coupling has only trivial equilibrium dynamics, the coupling induces complicated transitions to periodic, quasiperiodic, chaotic, and hyperchaotic behaviour. We study these transitions in detail for small number of individual nodes. For networks with more than five systems the transition to chaos occurs though stable three dimensional torus. Our results are confirmed by an experiment based on the coupled Duffing electronic circuits.