Polynomial maps with hidden complex dynamics

Xu Zhang*, Guanrong Chen

*Corresponding author for this work

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

16 Citations (Scopus)

Abstract

The dynamics of a class of one-dimensional polynomial maps are studied, and interesting dynamics are observed under certain conditions: the existence of periodic points with even periods except for one fixed point; the coexistence of two attractors, an attracting fixed point and a hidden attractor; the existence of a double period-doubling bifurcation, which is different from the classical period-doubling bifurcation of the Logistic map; the existence of Li-Yorke chaos. Furthermore, based on this one-dimensional map, the corresponding generalized Hénon map is investigated, and some interesting dynamics are found for certain parameter values: the coexistence of an attracting fixed point and a hidden attractor; the existence of Smale horseshoe for a subshift of finite type and also Li-Yorke chaos.
Original languageEnglish
Pages (from-to)2941-2954
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume24
Issue number6
DOIs
Publication statusPublished - Jun 2019

Research Keywords

  • Attractor
  • bifurcation
  • Li-Yorke chaos
  • polynomial map
  • Smale horseshoe
  • GENERALIZED HENON MAPS
  • LORENZ
  • DIFFEOMORPHISMS

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