Three-dimensional forced-damped dynamical systems with rich dynamics: bifurcations, chaos and unbounded solutions

Tomoyuki Miyaji, Hisashi Okamoto, Alexander Duncan Davidson Craik

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We consider certain autonomous three-dimensional dynamical systems that can arise in mechanical and fluid-dynamical contexts. Extending a previous study in Craik and Okamoto (2002), to include linear forcing and damping, we find that the four-leaf structure discovered in that paper, and unbounded orbits, persist, but may now be accompanied by three distinct period-doubling cascades to chaos, and by orbits that approach stable equilibrium points. This rich structure is investigated both analytically and numerically, distinguishing three main cases determined by the damping and forcing parameter values.
Original languageEnglish
JournalPhysica D: Nonlinear Phenomena
VolumeIn press
Early online date9 Sept 2015
DOIs
Publication statusPublished - 2015

Keywords

  • Three-dimensional dynamical system
  • Period-doubling cascades to chaos
  • Asymptotic analysis
  • Lyapunov function

Fingerprint

Dive into the research topics of 'Three-dimensional forced-damped dynamical systems with rich dynamics: bifurcations, chaos and unbounded solutions'. Together they form a unique fingerprint.

Cite this