On the Dynamics of a Model with Coexistence of Three Attractors: A Point, a Periodic Orbit and a Strange Attractor

Jaume Llibre, Claudia Valls

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1 Citation (Scopus)

Abstract

© 2017, Springer Science+Business Media Dordrecht. For a dynamical system described by a set of autonomous differential equations, an attractor can be either a point, or a periodic orbit, or even a strange attractor. Recently a new chaotic system with only one parameter has been presented where besides a point attractor and a chaotic attractor, it also has a coexisting attractor limit cycle which makes evident the complexity of such a system. We study using analytic tools the dynamics of such system. We describe its global dynamics near the infinity, and prove that it has no Darboux first integrals.
Original languageEnglish
Article number9
JournalMathematical Physics Analysis and Geometry
Volume20
Issue number2
DOIs
Publication statusPublished - 1 Jun 2017

Keywords

  • Chaotic system
  • Darboux integrability
  • Poincaré compactification

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