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Insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems

BACKGROUND: We have analysed large data sets consisting of tens of thousands of time series from three Type B laser systems: a semiconductor laser in a photonic integrated chip, a semiconductor laser subject to optical feedback from a long free-space-external-cavity, and a solid-state laser subject...

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Autores principales: McMahon, Christopher J., Toomey, Joshua P., Kane, Deb M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5570314/
https://www.ncbi.nlm.nih.gov/pubmed/28837602
http://dx.doi.org/10.1371/journal.pone.0181559
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author McMahon, Christopher J.
Toomey, Joshua P.
Kane, Deb M.
author_facet McMahon, Christopher J.
Toomey, Joshua P.
Kane, Deb M.
author_sort McMahon, Christopher J.
collection PubMed
description BACKGROUND: We have analysed large data sets consisting of tens of thousands of time series from three Type B laser systems: a semiconductor laser in a photonic integrated chip, a semiconductor laser subject to optical feedback from a long free-space-external-cavity, and a solid-state laser subject to optical injection from a master laser. The lasers can deliver either constant, periodic, pulsed, or chaotic outputs when parameters such as the injection current and the level of external perturbation are varied. The systems represent examples of experimental nonlinear systems more generally and cover a broad range of complexity including systematically varying complexity in some regions. METHODS: In this work we have introduced a new procedure for semi-automatically interrogating experimental laser system output power time series to calculate the correlation dimension (CD) using the commonly adopted Grassberger-Proccacia algorithm. The new CD procedure is called the ‘minimum gradient detection algorithm’. A value of minimum gradient is returned for all time series in a data set. In some cases this can be identified as a CD, with uncertainty. FINDINGS: Applying the new ‘minimum gradient detection algorithm’ CD procedure, we obtained robust measurements of the correlation dimension for many of the time series measured from each laser system. By mapping the results across an extended parameter space for operation of each laser system, we were able to confidently identify regions of low CD (CD < 3) and assign these robust values for the correlation dimension. However, in all three laser systems, we were not able to measure the correlation dimension at all parts of the parameter space. Nevertheless, by mapping the staged progress of the algorithm, we were able to broadly classify the dynamical output of the lasers at all parts of their respective parameter spaces. For two of the laser systems this included displaying regions of high-complexity chaos and dynamic noise. These high-complexity regions are differentiated from regions where the time series are dominated by technical noise. This is the first time such differentiation has been achieved using a CD analysis approach. CONCLUSIONS: More can be known of the CD for a system when it is interrogated in a mapping context, than from calculations using isolated time series. This has been shown for three laser systems and the approach is expected to be useful in other areas of nonlinear science where large data sets are available and need to be semi-automatically analysed to provide real dimensional information about the complex dynamics. The CD/minimum gradient algorithm measure provides additional information that complements other measures of complexity and relative complexity, such as the permutation entropy; and conventional physical measurements.
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spelling pubmed-55703142017-09-09 Insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems McMahon, Christopher J. Toomey, Joshua P. Kane, Deb M. PLoS One Research Article BACKGROUND: We have analysed large data sets consisting of tens of thousands of time series from three Type B laser systems: a semiconductor laser in a photonic integrated chip, a semiconductor laser subject to optical feedback from a long free-space-external-cavity, and a solid-state laser subject to optical injection from a master laser. The lasers can deliver either constant, periodic, pulsed, or chaotic outputs when parameters such as the injection current and the level of external perturbation are varied. The systems represent examples of experimental nonlinear systems more generally and cover a broad range of complexity including systematically varying complexity in some regions. METHODS: In this work we have introduced a new procedure for semi-automatically interrogating experimental laser system output power time series to calculate the correlation dimension (CD) using the commonly adopted Grassberger-Proccacia algorithm. The new CD procedure is called the ‘minimum gradient detection algorithm’. A value of minimum gradient is returned for all time series in a data set. In some cases this can be identified as a CD, with uncertainty. FINDINGS: Applying the new ‘minimum gradient detection algorithm’ CD procedure, we obtained robust measurements of the correlation dimension for many of the time series measured from each laser system. By mapping the results across an extended parameter space for operation of each laser system, we were able to confidently identify regions of low CD (CD < 3) and assign these robust values for the correlation dimension. However, in all three laser systems, we were not able to measure the correlation dimension at all parts of the parameter space. Nevertheless, by mapping the staged progress of the algorithm, we were able to broadly classify the dynamical output of the lasers at all parts of their respective parameter spaces. For two of the laser systems this included displaying regions of high-complexity chaos and dynamic noise. These high-complexity regions are differentiated from regions where the time series are dominated by technical noise. This is the first time such differentiation has been achieved using a CD analysis approach. CONCLUSIONS: More can be known of the CD for a system when it is interrogated in a mapping context, than from calculations using isolated time series. This has been shown for three laser systems and the approach is expected to be useful in other areas of nonlinear science where large data sets are available and need to be semi-automatically analysed to provide real dimensional information about the complex dynamics. The CD/minimum gradient algorithm measure provides additional information that complements other measures of complexity and relative complexity, such as the permutation entropy; and conventional physical measurements. Public Library of Science 2017-08-24 /pmc/articles/PMC5570314/ /pubmed/28837602 http://dx.doi.org/10.1371/journal.pone.0181559 Text en © 2017 McMahon et al http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
McMahon, Christopher J.
Toomey, Joshua P.
Kane, Deb M.
Insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems
title Insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems
title_full Insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems
title_fullStr Insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems
title_full_unstemmed Insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems
title_short Insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems
title_sort insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5570314/
https://www.ncbi.nlm.nih.gov/pubmed/28837602
http://dx.doi.org/10.1371/journal.pone.0181559
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