Efficient algorithm for detecting unstable periodic orbits in chaotic systems

Ruslan L. Davidchack, Ying Cheng Lai

Research output: Contribution to journalArticlepeer-review

85 Scopus citations


We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of an iterative scheme and an effective technique for selecting initial points. The iterative scheme is based on the semi-implicit Euler method, which has both fast and global convergence, and only a small number of initial points is sufficient to detect all unstable periodic orbits of a given period. The power of our method is illustrated by numerical examples of both two- and four-dimensional maps.

Original languageEnglish (US)
Pages (from-to)6172-6175
Number of pages4
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number5
StatePublished - 1999
Externally publishedYes

ASJC Scopus subject areas

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


Dive into the research topics of 'Efficient algorithm for detecting unstable periodic orbits in chaotic systems'. Together they form a unique fingerprint.

Cite this