TY - GEN A1 - Perlikowski, Przemyslaw A1 - Yanchuk, Serhiy A1 - Wolfrum, Matthias A1 - Stefanski, Andrzej A1 - Mosiolek, Przemyslaw A1 - Kapitaniak, Tomasz T1 - Routes to complex dynamics in a ring of unidirectionally coupled systems N2 - We study 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 behavior. We study these transitions in detail for small and large numbers of oscillators. Particular attention is paid to the role of unstable periodic solutions for the appearance of chaotic rotating waves, spatiotemporal structures and the Eckhaus effect for a large number of oscillators. Our analytical and numerical results are confirmed by a simple experiment based on the electronic implementation of coupled Duffing oscillators. KW - coupled systems KW - unidirectional coupling KW - synchronization KW - Duffing oscillator KW - electric circuit KW - Eckhaus Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/664 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-6649 ER -