A Four-Leaf Chaotic Attractor of a Three-Dimensional Dynamical System

Tomoyuki Miyaji*, Hisashi Okamoto, Alexander Duncan Davidson Craik

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


A three-dimensional autonomous dynamical system proposed by Pehlivan is untypical in simultaneously possessing both unbounded and chaotic solutions. Here, this topic is studied in some depth, both numerically and analytically. We find, by standard methods, that four-leaf chaotic orbits result from a period-doubling cascade; we identify unstable fixed points and both stable and unstable periodic orbits; and we examine how initial data determines whether orbits approach infinity or a stable periodic orbit. Further, we describe and apply a strict numerical verification method that rigorously proves the existence of sequences of period doublings.

Original languageEnglish
Article number1530003
Number of pages21
JournalInternational Journal of Bifurcation and Chaos
Issue number2
Publication statusPublished - Feb 2015


  • Three-dimensional dynamical system
  • period-doubling cascades to chaos
  • numerical verification


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