Towards complete detection of unstable periodic orbits in chaotic systems

Ruslan L. Davidchack, Ying-Cheng Lai, Aaron Klebanoff, Erik M. Bollt

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

We present a rigorous analysis and numerical evidence indicating that a recently developed methodology for detecting unstable periodic orbits is capable of yielding all orbits up to periods limited only by the computer precision. In particular, we argue that an efficient convergence to every periodic orbit can be achieved and the basin of attraction can be made finite and accessible for typical or particularly chosen initial conditions. (C) 2001 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)99-104
Number of pages6
JournalPhysics Letters A
Volume287
Issue number1-2
DOIs
Publication statusPublished - 20 Aug 2001

Keywords

  • dynamical-systems
  • strange attractor
  • ring cavity
  • map

Cite this

Davidchack, R. L., Lai, Y-C., Klebanoff, A., & Bollt, E. M. (2001). Towards complete detection of unstable periodic orbits in chaotic systems. Physics Letters A, 287(1-2), 99-104. https://doi.org/10.1016/S0375-9601(01)00463-7