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Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems

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 Ginzbur...

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Published in:	Chaos (Woodbury, N.Y.) N.Y.), 2015-03, Vol.25 (3), p.033113-033113
Main Authors:	Yanchuk, S, Perlikowski, P, Wolfrum, M, Stefański, A, Kapitaniak, T
Format:	Article
Language:	English
Subjects:	Algorithms AMPLITUDES CHAOS THEORY CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Computer Simulation CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY COUPLING EQUATIONS Feedback GINZBURG-LANDAU THEORY INTERACTIONS MATHEMATICAL SOLUTIONS Models, Theoretical Nonlinear Dynamics OSCILLATORS Oscillometry - methods SPACE DEPENDENCE Spatio-Temporal Analysis TIME DEPENDENCE
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creator	Yanchuk, S Perlikowski, P Wolfrum, M Stefański, A Kapitaniak, T
description	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.
doi_str_mv	10.1063/1.4915941
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subjects	Algorithms AMPLITUDES CHAOS THEORY CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Computer Simulation CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY COUPLING EQUATIONS Feedback GINZBURG-LANDAU THEORY INTERACTIONS MATHEMATICAL SOLUTIONS Models, Theoretical Nonlinear Dynamics OSCILLATORS Oscillometry - methods SPACE DEPENDENCE Spatio-Temporal Analysis TIME DEPENDENCE
title	Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems
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