title: Routes to complex dynamics in a ring of unidirectionally coupled systems.
abstract: 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.
authors.affiliation: Institute of Mathematics, Humboldt University of Berlin, Unter den Linden 6, 10099 Berlin, Germany. przemyslaw.perlikowski@p.lodz.pl
authors.forename: P
authors.initials: P
authors.lastname: Perlikowski
authors.forename: S
authors.initials: S
authors.lastname: Yanchuk
authors.forename: M
authors.initials: M
authors.lastname: Wolfrum
authors.forename: A
authors.initials: A
authors.lastname: Stefanski
authors.forename: P
authors.initials: P
authors.lastname: Mosiolek
authors.forename: T
authors.initials: T
authors.lastname: Kapitaniak
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D004581:Electronics; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D013997:Time Factors