Frequency locking and complex dynamics near a periodically forced robust heteroclinic cycle

J. H.P. Dawes, Tsung-Lung Tsai

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Robust heteroclinic cycles occur naturally in many classes of nonlinear differential equations with invariant hyperplanes. In particular they occur frequently in models for ecological dynamics and fluid mechanical instabilities. We consider the effect of small-amplitude time-periodic forcing and describe how to reduce the dynamics to a two-dimensional map. In the limit where the heteroclinic cycle loses asymptotic stability, intervals of frequency locking appear. In the opposite limit, where the heteroclinic cycle becomes strongly stable, the dynamics remains chaotic and no frequency locking is observed.

Original languageEnglish
Article number055201
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume74
Issue number5
DOIs
Publication statusPublished - 2006 Nov 13

Fingerprint

Frequency Locking
Heteroclinic Cycle
Complex Dynamics
locking
cycles
hyperplanes
Periodic Forcing
Chaotic Dynamics
Hyperplane
Asymptotic Stability
Nonlinear Differential Equations
differential equations
intervals
Fluid
Interval
Invariant
fluids
Model

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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