title: Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems.
abstract: 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 and close-by solutions in the limit of a large number of nodes. Studying numerically an example of unidirectionally coupled Duffing oscillators, we observe a coupling induced transition to collective spatio-temporal chaos, which can be understood using the derived amplitude equations.
authors.affiliation: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.
authors.forename: S
authors.initials: S
authors.lastname: Yanchuk
authors.affiliation: Division of Dynamics, Technical University of Lodz, 90-924 Lodz, Poland.
authors.forename: P
authors.initials: P
authors.lastname: Perlikowski
authors.affiliation: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.
authors.forename: M
authors.initials: M
authors.lastname: Wolfrum
authors.affiliation: Division of Dynamics, Technical University of Lodz, 90-924 Lodz, Poland.
authors.forename: A
authors.initials: A
authors.lastname: Stefański
authors.affiliation: Division of Dynamics, Technical University of Lodz, 90-924 Lodz, Poland.
authors.forename: T
authors.initials: T
authors.lastname: Kapitaniak
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D062211:Spatio-Temporal Analysis