Global dynamics of the Rikitake system

Jaume Llibre, Marcelo Messias

Research output: Contribution to journalArticleResearchpeer-review

50 Citations (Scopus)

Abstract

The Rikitake system is a three dimensional vector field obtained experimentally from a two-disk dynamo apparatus, which models the geomagnetic field and is used to explain the known irregular switch in its polarity. The system has a 3-dimensional Lorenz type chaotic attractor around its two singular points. However this attractor is not bounded by any ellipsoidal surface as in the Lorenz attractor. In this paper, by using the Poincaré compactification for polynomial vector fields in R3 we study the dynamics of the Rikitake system at infinity, showing that there are orbits which escape to, or come from, infinity, instead of going towards the attractor. Moreover we study, for particular values of the parameters, the flow over two invariant planes, and describe the global flow of the system when it has two independent first integrals and thus is completely integrable. The global analysis performed, allows us to give a numerical description of the creation of Rikitake attractor. © 2008 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)241-252
JournalPhysica D: Nonlinear Phenomena
Volume238
DOIs
Publication statusPublished - 1 Jan 2009

Keywords

  • Geodynamo
  • Lorenz attractor
  • Poincaré compactification
  • Rikitake attractor
  • Strange attractor creation
  • Unbounded orbits

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