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On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators

Authors
  • Gonchenko, AS
  • Gonchenko, SV
  • Kazakov, AO
  • Turaev, DV
Publication Date
Feb 04, 2017
Identifiers
DOI: 10.1016/j.physd.2017.02.002
OAI: oai:spiral.imperial.ac.uk:10044/1/50656
Source
Spiral - Imperial College Digital Repository
Keywords
License
Unknown

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.

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