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

A. S. Gonchenko, S. V. Gonchenko, A. O. Kazakov, D. V. Turaev

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


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.

Original languageEnglish
Pages (from-to)45-57
Number of pages13
JournalPhysica D: Nonlinear Phenomena
StatePublished - 1 Jul 2017
Externally publishedYes


  • Attractor
  • Elliptic point
  • Repeller
  • Reversible system
  • Symmetry-breaking bifurcation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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