The Chaotic Saddle in the Lozi Map, Autonomous and Nonautonomous Versions

Carlos Lopesino, Francisco Balibrea, Stephen R Wiggins, Ana M Mancho

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)
204 Downloads (Pure)

Abstract

In this paper, we prove the existence of a chaotic saddle for a piecewise-linear map of the plane, referred to as the Lozi map. We study the Lozi map in its orientation and area preserving version. First, we consider the autonomous version of the Lozi map to which we apply the Conley–Moser conditions to obtain the proof of a chaotic saddle. Then we generalize the Lozi map on a nonautonomous version and we prove that the first and the third Conley–Moser conditions are satisfied, which imply the existence of a chaotic saddle. Finally, we numerically demonstrate how the structure of this nonautonomous chaotic saddle varies as parameters are varied.
Original languageEnglish
Article number1550184
Number of pages18
JournalInternational Journal of Bifurcation and Chaos
Volume25
Issue number13
DOIs
Publication statusPublished - 15 Dec 2015

Keywords

  • Chaotic saddle
  • autonomous dynamics
  • nonautonomous dynamics
  • Lozi map
  • Conley–Moser conditions

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