https://doi.org/10.1140/epjst/e2020-900276-4
Regular Article
Stability of the 3-torus solution in a ring of coupled Duffing oscillators
1
Department of Strength of Materials, Lodz University of Technology,
ul. Stefanowskiego 1/15
Lodz, Poland
2
Division of Dynamics, Lodz University of Technology,
ul. Stefanowskiego 1/15
Lodz, Poland
a e-mail: andrzej.stefanski@p.lodz.pl
Received:
8
December
2019
Accepted:
8
June
2020
Published online: 28 September 2020
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.
© The Author(s) 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
