On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators
File(s)
Accepted version
Author(s)
Gonchenko, AS
Gonchenko, SV
Kazakov, AO
Turaev, DV
Type
Journal Article
Abstract
A one-parameter family of time-reversible systems on three-dimensional torus is considered. It is shown that the dynamics is not conservative, namely the attractor and repeller intersect but not coincide. We explain this as the manifestation of the so-called mixed dynamics phenomenon which corresponds to a persistent intersection of the closure of the stable periodic orbits and the closure of the completely unstable periodic orbits. We search for the stable and unstable periodic orbits indirectly, by finding non-conservative saddle periodic orbits and heteroclinic connections between them. In this way, we are able to claim the existence of mixed dynamics for a large range of parameter values. We investigate local and global bifurcations that can be used for the detection of mixed dynamics.
Date Issued
2017-03-30
Date Acceptance
2017-02-04
Citation
Physica D: Nonlinear Phenomena, 2017, 350, pp.45-57
ISSN
0167-2789
Publisher
Elsevier
Start Page
45
End Page
57
Journal / Book Title
Physica D: Nonlinear Phenomena
Volume
350
Copyright Statement
© 2017 Elsevier B.V. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000401876300004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Physics, Multidisciplinary
Physics, Mathematical
Mathematics
Physics
Reversible system
Attractor
Repeller
Elliptic point
Symmetry-breaking bifurcation
DISSIPATIVE BEHAVIOR
STRANGE ATTRACTORS
REVERSIBLE-SYSTEMS
SYMMETRY
MAPS
Publication Status
Published