Periodic orbits and their bifurcations in 3-D maps with separate third iterate

Anna Agliari, Daniéle Fournier-Prunaret, Abdel Kaddous Taha

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

We consider a class of three-dimensional maps T having the property that their third iterate has separate components. We show that the cycles of T can be obtained by those of a one-dimensional map (one of the components of T 3) and we give a complete classification of such cycles. The local bifurcations of the cycles of T are studied as well, showing that they are of co-dimension 3, since at the bifurcation value three eigenvalues simultaneously cross the unit circle. To illustrate the obtained results we consider as an example a delayed logistic map.
Original languageEnglish
Title of host publicationGlobal Analysis of Dynamic Models in Economics and Finance. Essays in Honour of Laura Gardini
EditorsG.I. Bischi, C. Chiarella, I. Sushko
Pages397-427
Number of pages31
DOIs
Publication statusPublished - 2012

Keywords

  • 3D maps
  • Delayed logistic map
  • Local bifurcations
  • Multistability

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