Numerical study of coexisting attractors for the Hénon map

Zbigniew Galias, Warwick Tucker

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11 Citations (Scopus)

Abstract

The question of coexisting attractors for the Hénon map is studied numerically by performing an exhaustive search in the parameter space. As a result, several parameter values for which more than two attractors coexist are found. Using tools from interval analysis, we show rigorously that the attractors exist. In the case of periodic orbits, we verify that they are stable, and thus proper sinks. Regions of existence in parameter space of the found sinks are located using a continuation method; the basins of attraction are found numerically.

Original languageEnglish
Article number1330025
JournalInternational Journal of Bifurcation and Chaos
Volume23
Issue number7
DOIs
Publication statusPublished - Jul 2013
Externally publishedYes

Keywords

  • coexisting attractors
  • Hénon map
  • interval arithmetic
  • periodic orbit

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