Unstable periodic orbits in the Lorenz attractor

Bruce M. Boghosian, Aaron W Brown, Jonas Lätt, Hui Tang, Luis M. Fazendeiro, Peter V. Coveney

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We apply a new method for the determination of periodic orbits of general dynamical systems to the Lorenz equations. The accuracy of the expectation values obtained using this approach is shown to be much larger and have better convergence properties than the more traditional approach of time averaging over a generic orbit. Finally, we discuss the relevance of the present work to the computation of unstable periodic orbits of the driven Navier-Stokes equations, which can be simulated using the lattice Boltzmann method.

Original languageEnglish (US)
Pages (from-to)2345-2353
Number of pages9
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume369
Issue number1944
DOIs
StatePublished - Jun 13 2011

Keywords

  • Dynamical systems
  • Lorenz equations
  • Navier-Stokes
  • Periodic orbits

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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