WIAS Preprint No. 2070, (2015)
Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems
Authors
- Yanchuk, Serhiy
- Perlikowski, Przemysław
- Wolfrum, Matthias
ORCID: 0000-0002-4278-2675 - Stefański, Andrzej
- Kapitaniak, Tomasz
Keywords
- coupled oscillators, amplitude equations, Ginzburg-Landau equation, spatio-temporal chaos
DOI
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.
Appeared in
- Chaos, 25 (2015) pp. 033113/1--033113/8.
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