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Stability of the 3-torus solution in a ring of coupled Duffing oscillators

Authors
  • Borkowski, L.1
  • Stefanski, A.2
  • 1 Lodz University of Technology, ul. Stefanowskiego 1/15, Lodz, Poland , Lodz (Poland)
  • 2 Division of Dynamics, Lodz University of Technology, ul. Stefanowskiego 1/15, Lodz, Poland , Lodz (Poland)
Type
Published Article
Journal
The European Physical Journal Special Topics
Publisher
Springer Berlin Heidelberg
Publication Date
Sep 28, 2020
Volume
229
Issue
12-13
Pages
2249–2259
Identifiers
DOI: 10.1140/epjst/e2020-900276-4
Source
Springer Nature
License
Green

Abstract

The dynamics of the ring of unidirectionally coupled single-well Duffing oscillators is analyzed in numerical simulation for identical nodal oscillators. The research is concentrated on the existence of the stable 3D torus attractor in this system. It is shown that 3-frequency quasi-periodicity can be robustly stable in wide range of parameters of the system under consideration. As an explanation of this stability, the conjecture on the coexistence and superposition of two independent effects characterized with irrational frequencies, i.e., the classical Newhouse, Ruelle and Takens scenario and rotating wave flow, is formulated.

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