Unstable periodic orbits in the Lorenz attractor

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

doi:10.1098/rsta.2011.0067

Unstable periodic orbits in the Lorenz attractor

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

Mathematics

Research output: Contribution to journal › Article › peer-review

6 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 language	English (US)
Pages (from-to)	2345-2353
Number of pages	9
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	369
Issue number	1944
DOIs	https://doi.org/10.1098/rsta.2011.0067
State	Published - 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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10.1098/rsta.2011.0067

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AU - Boghosian, Bruce M.

AU - Brown, Aaron W

AU - Lätt, Jonas

AU - Tang, Hui

AU - Fazendeiro, Luis M.

AU - Coveney, Peter V.

PY - 2011/6/13

Y1 - 2011/6/13

N2 - 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.

AB - 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.

KW - Dynamical systems

KW - Lorenz equations

KW - Navier-Stokes

KW - Periodic orbits

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ER -

Unstable periodic orbits in the Lorenz attractor

Abstract

Keywords

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