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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:
;  [1];  [2];  [3]; ;  [2]
  1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin (Germany)
  2. Division of Dynamics, Technical University of Lodz, 90-924 Lodz (Poland)
  3. (Singapore)
Publication Date:
OSTI Identifier:
22402540
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; AMPLITUDES; CHAOS THEORY; COUPLING; EQUATIONS; GINZBURG-LANDAU THEORY; INTERACTIONS; MATHEMATICAL SOLUTIONS; OSCILLATORS; SPACE DEPENDENCE; TIME DEPENDENCE

Citation Formats

Yanchuk, S., Wolfrum, M., Perlikowski, P., Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore, Singapore 117576, Stefański, A., and Kapitaniak, T. Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems. United States: N. p., 2015. Web. doi:10.1063/1.4915941.
Yanchuk, S., Wolfrum, M., Perlikowski, P., Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore, Singapore 117576, Stefański, A., & Kapitaniak, T. Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems. United States. doi:10.1063/1.4915941.
Yanchuk, S., Wolfrum, M., Perlikowski, P., Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore, Singapore 117576, Stefański, A., and Kapitaniak, T. Sun . "Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems". United States. doi:10.1063/1.4915941.
@article{osti_22402540,
title = {Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems},
author = {Yanchuk, S. and Wolfrum, M. and Perlikowski, P. and Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore, Singapore 117576 and Stefański, A. and Kapitaniak, T.},
abstractNote = {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 = {10.1063/1.4915941},
journal = {Chaos (Woodbury, N. Y.)},
number = 3,
volume = 25,
place = {United States},
year = {Sun Mar 15 00:00:00 EDT 2015},
month = {Sun Mar 15 00:00:00 EDT 2015}
}