Geometric method for forming periodic orbits in the Lorenz system

S. B. Nicholson; Eun Jin Kim

doi:10.1088/0031-8949/91/4/044006

Geometric method for forming periodic orbits in the Lorenz system

S. B. Nicholson, Eun Jin Kim

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

2 Citations (Scopus)

72 Downloads (Pure)

Abstract

Many systems in nature are out of equilibrium and irreversible. The non-detailed balance observable representation (NOR) provides a useful methodology for understanding the evolution of such non-equilibrium complex systems, by mapping out the correlation between two states to a metric space where a small distance represents a strong correlation [1]. In this paper, we present the first application of the NOR to a continuous system and demonstrate its utility in controlling chaos. Specifically, we consider the evolution of a continuous system governed by the Lorenz equation and calculate the NOR by following a sufficient number of trajectories. We then show how to control chaos by converting chaotic orbits to periodic orbits by utilizing the NOR. We further discuss the implications of our method for potential applications given the key advantage that this method makes no assumptions of the underlying equations of motion and is thus extremely general.

Original language	English
Article number	044006
Number of pages	7
Journal	Physica Scripta
Volume	91
Issue number	4
DOIs	https://doi.org/10.1088/0031-8949/91/4/044006
Publication status	Published - 30 Mar 2016
Externally published	Yes

Bibliographical note

This is an author-created, un-copyedited version of an article accepted for publication/published in Physica Scripta. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0031-8949/91/4/044006

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

Keywords

Chaos
Far from equilibrium
Non-equilibrium
Periodic orbit
Spectral theory

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics
Mathematical Physics
Condensed Matter Physics
General Physics and Astronomy

Access to Document

10.1088/0031-8949/91/4/044006

Post-PrintAccepted author manuscript, 5.53 MBLicence: Unspecified

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N2 - Many systems in nature are out of equilibrium and irreversible. The non-detailed balance observable representation (NOR) provides a useful methodology for understanding the evolution of such non-equilibrium complex systems, by mapping out the correlation between two states to a metric space where a small distance represents a strong correlation [1]. In this paper, we present the first application of the NOR to a continuous system and demonstrate its utility in controlling chaos. Specifically, we consider the evolution of a continuous system governed by the Lorenz equation and calculate the NOR by following a sufficient number of trajectories. We then show how to control chaos by converting chaotic orbits to periodic orbits by utilizing the NOR. We further discuss the implications of our method for potential applications given the key advantage that this method makes no assumptions of the underlying equations of motion and is thus extremely general.

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Geometric method for forming periodic orbits in the Lorenz system

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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