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Sensitivity of long periodic orbits of chaotic systems

Sensitivity of long periodic orbits of chaotic systems
Sensitivity of long periodic orbits of chaotic systems
The properties of long, numerically-determined periodic orbits of two low-dimensional chaotic systems, the Lorenz equations and the Kuramoto-Sivashinsky system in a minimal-domain configuration, are examined. The primary question is to establish whether the sensitivity of period averaged quantities with respect to parameter perturbations computed over long orbits can be used as a sufficiently good proxy for the response of the chaotic state to finite-amplitude parameter perturbations. To address this question, an inventory of thousands of orbits at least two-order of magnitude longer than the shortest admissible cycles is constructed. The expectation of period averages, Floquet exponents and sensitivities over such set is then obtained. It is shown that all these quantities converge to a limiting value as the orbit period is increased. However, while period averages and Floquet exponents appear to converge to analogous quantities computed from chaotic trajectories, the limiting value of the sensitivity is not necessarily consistent with the response of the chaotic state, similar to observations made with other shadowing algorithms.
1539-3755
Lasagna, Davide
0340a87f-f323-40fb-be9f-6de101486b24
Lasagna, Davide
0340a87f-f323-40fb-be9f-6de101486b24

Lasagna, Davide (2020) Sensitivity of long periodic orbits of chaotic systems. Physical Review E. (In Press)

Record type: Article

Abstract

The properties of long, numerically-determined periodic orbits of two low-dimensional chaotic systems, the Lorenz equations and the Kuramoto-Sivashinsky system in a minimal-domain configuration, are examined. The primary question is to establish whether the sensitivity of period averaged quantities with respect to parameter perturbations computed over long orbits can be used as a sufficiently good proxy for the response of the chaotic state to finite-amplitude parameter perturbations. To address this question, an inventory of thousands of orbits at least two-order of magnitude longer than the shortest admissible cycles is constructed. The expectation of period averages, Floquet exponents and sensitivities over such set is then obtained. It is shown that all these quantities converge to a limiting value as the orbit period is increased. However, while period averages and Floquet exponents appear to converge to analogous quantities computed from chaotic trajectories, the limiting value of the sensitivity is not necessarily consistent with the response of the chaotic state, similar to observations made with other shadowing algorithms.

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Accepted/In Press date: 3 November 2020

Identifiers

Local EPrints ID: 444952
URI: http://eprints.soton.ac.uk/id/eprint/444952
ISSN: 1539-3755
PURE UUID: fcc62be1-8e30-43df-aa3b-539b0f3bd1cd
ORCID for Davide Lasagna: ORCID iD orcid.org/0000-0002-6501-6041

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Date deposited: 12 Nov 2020 17:33
Last modified: 13 Dec 2021 03:11

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