Experimentally Viable Techniques for Accessing Coexisting Attractors Correlated with Lyapunov Exponents

Universal, predictive attractor patterns configured by Lyapunov exponents (LEs) as a function of the control parameter are shown to characterize periodic windows in chaos just as in attractors, using a coherent model of the laser with injected signal. One such predictive pattern, the symmetric-like...

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Autores principales:	Joshua Ray Hall, Erikk Kenneth Tilus Burton, Dylan Michael Chapman, Donna Kay Bandy
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	nonlinear system coexisting attractors control methods multistability Lyapunov exponents optically driven laser Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/79cb29b17b9e4b9294781d94374b9c11
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spelling	oai:doaj.org-article:79cb29b17b9e4b9294781d94374b9c112021-11-11T15:00:22ZExperimentally Viable Techniques for Accessing Coexisting Attractors Correlated with Lyapunov Exponents10.3390/app112199052076-3417https://doaj.org/article/79cb29b17b9e4b9294781d94374b9c112021-10-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/21/9905https://doaj.org/toc/2076-3417Universal, predictive attractor patterns configured by Lyapunov exponents (LEs) as a function of the control parameter are shown to characterize periodic windows in chaos just as in attractors, using a coherent model of the laser with injected signal. One such predictive pattern, the symmetric-like bubble, foretells of an imminent bifurcation. With a slight decrease in the gain parameter, we find the symmetric-like bubble changes to a curved trajectory of two equal LEs in one attractor, while an increase in the gain reverses this process in another attractor. We generalize the power-shift method for accessing coexisting attractors or periodic windows by augmenting the technique with an interim parameter shift that optimizes attractor retrieval. We choose the gain as our parameter to interim shift. When interim gain-shift results are compared with LE patterns for a specific gain, we find critical points on the LE spectra where the attractor is unlikely to survive the gain shift. Noise and lag effects obscure the power shift minimally for large domain attractors. Small domain attractors are less accessible. The power-shift method in conjunction with the interim parameter shift is attractive because it can be experimentally applied without significant or long-lasting modifications to the experimental system.Joshua Ray HallErikk Kenneth Tilus BurtonDylan Michael ChapmanDonna Kay BandyMDPI AGarticlenonlinear systemcoexisting attractorscontrol methodsmultistabilityLyapunov exponentsoptically driven laserTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 9905, p 9905 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	nonlinear system coexisting attractors control methods multistability Lyapunov exponents optically driven laser Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	nonlinear system coexisting attractors control methods multistability Lyapunov exponents optically driven laser Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Joshua Ray Hall Erikk Kenneth Tilus Burton Dylan Michael Chapman Donna Kay Bandy Experimentally Viable Techniques for Accessing Coexisting Attractors Correlated with Lyapunov Exponents
description	Universal, predictive attractor patterns configured by Lyapunov exponents (LEs) as a function of the control parameter are shown to characterize periodic windows in chaos just as in attractors, using a coherent model of the laser with injected signal. One such predictive pattern, the symmetric-like bubble, foretells of an imminent bifurcation. With a slight decrease in the gain parameter, we find the symmetric-like bubble changes to a curved trajectory of two equal LEs in one attractor, while an increase in the gain reverses this process in another attractor. We generalize the power-shift method for accessing coexisting attractors or periodic windows by augmenting the technique with an interim parameter shift that optimizes attractor retrieval. We choose the gain as our parameter to interim shift. When interim gain-shift results are compared with LE patterns for a specific gain, we find critical points on the LE spectra where the attractor is unlikely to survive the gain shift. Noise and lag effects obscure the power shift minimally for large domain attractors. Small domain attractors are less accessible. The power-shift method in conjunction with the interim parameter shift is attractive because it can be experimentally applied without significant or long-lasting modifications to the experimental system.
format	article
author	Joshua Ray Hall Erikk Kenneth Tilus Burton Dylan Michael Chapman Donna Kay Bandy
author_facet	Joshua Ray Hall Erikk Kenneth Tilus Burton Dylan Michael Chapman Donna Kay Bandy
author_sort	Joshua Ray Hall
title	Experimentally Viable Techniques for Accessing Coexisting Attractors Correlated with Lyapunov Exponents
title_short	Experimentally Viable Techniques for Accessing Coexisting Attractors Correlated with Lyapunov Exponents
title_full	Experimentally Viable Techniques for Accessing Coexisting Attractors Correlated with Lyapunov Exponents
title_fullStr	Experimentally Viable Techniques for Accessing Coexisting Attractors Correlated with Lyapunov Exponents
title_full_unstemmed	Experimentally Viable Techniques for Accessing Coexisting Attractors Correlated with Lyapunov Exponents
title_sort	experimentally viable techniques for accessing coexisting attractors correlated with lyapunov exponents
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/79cb29b17b9e4b9294781d94374b9c11
work_keys_str_mv	AT joshuarayhall experimentallyviabletechniquesforaccessingcoexistingattractorscorrelatedwithlyapunovexponents AT erikkkennethtilusburton experimentallyviabletechniquesforaccessingcoexistingattractorscorrelatedwithlyapunovexponents AT dylanmichaelchapman experimentallyviabletechniquesforaccessingcoexistingattractorscorrelatedwithlyapunovexponents AT donnakaybandy experimentallyviabletechniquesforaccessingcoexistingattractorscorrelatedwithlyapunovexponents
_version_	1718437901339983872

Experimentally Viable Techniques for Accessing Coexisting Attractors Correlated with Lyapunov Exponents

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