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Velocity–Amplitude Relationship in the Gray–Scott Autowave Model in Isolated Conditions

[Image: see text] Velocity and amplitude are two basic characteristics of any autowave, and their relationship reflects the internal regulation of the autowave system. This study proposes an approach to approximately estimate steady velocity–amplitude (VA) relation without deriving separate formulas...

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Autor principal: Tokarev, Alexey A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: American Chemical Society 2019
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6740189/
https://www.ncbi.nlm.nih.gov/pubmed/31528796
http://dx.doi.org/10.1021/acsomega.9b01338
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author Tokarev, Alexey A.
author_facet Tokarev, Alexey A.
author_sort Tokarev, Alexey A.
collection PubMed
description [Image: see text] Velocity and amplitude are two basic characteristics of any autowave, and their relationship reflects the internal regulation of the autowave system. This study proposes an approach to approximately estimate steady velocity–amplitude (VA) relation without deriving separate formulas for V and A. The approach presumes constructing an ansatz which represents the “petal” form of phase trajectory and contains V, A, and a free parameter (parameters). After substituting this ansatz, integration of model equations leads to a VA relation analytically. A free parameter (parameters) can be determined by comparing the analytical VA relation to the numerical data. As an example, we used the simplest autowave model possessing threshold, that is, the Gray–Scott model (cubic autocatalysis with linear inhibition) in isolated conditions with an immobilized precursor and a diffusible reactant. For all values of the inhibition rate constant allowing autowave solution (i.e., except approaching zero), the free parameter of ansatz belongs to a narrow interval has little effect on VA relation and can be regarded as fixed. Assumption of precursor immobilization does not influence the results qualitatively. This approach will be useful in investigations of more complex active media systems in biochemistry, combustion, and disease control.
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spelling pubmed-67401892019-09-16 Velocity–Amplitude Relationship in the Gray–Scott Autowave Model in Isolated Conditions Tokarev, Alexey A. ACS Omega [Image: see text] Velocity and amplitude are two basic characteristics of any autowave, and their relationship reflects the internal regulation of the autowave system. This study proposes an approach to approximately estimate steady velocity–amplitude (VA) relation without deriving separate formulas for V and A. The approach presumes constructing an ansatz which represents the “petal” form of phase trajectory and contains V, A, and a free parameter (parameters). After substituting this ansatz, integration of model equations leads to a VA relation analytically. A free parameter (parameters) can be determined by comparing the analytical VA relation to the numerical data. As an example, we used the simplest autowave model possessing threshold, that is, the Gray–Scott model (cubic autocatalysis with linear inhibition) in isolated conditions with an immobilized precursor and a diffusible reactant. For all values of the inhibition rate constant allowing autowave solution (i.e., except approaching zero), the free parameter of ansatz belongs to a narrow interval has little effect on VA relation and can be regarded as fixed. Assumption of precursor immobilization does not influence the results qualitatively. This approach will be useful in investigations of more complex active media systems in biochemistry, combustion, and disease control. American Chemical Society 2019-08-28 /pmc/articles/PMC6740189/ /pubmed/31528796 http://dx.doi.org/10.1021/acsomega.9b01338 Text en Copyright © 2019 American Chemical Society This is an open access article published under a Creative Commons Attribution (CC-BY) License (http://pubs.acs.org/page/policy/authorchoice_ccby_termsofuse.html) , which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
spellingShingle Tokarev, Alexey A.
Velocity–Amplitude Relationship in the Gray–Scott Autowave Model in Isolated Conditions
title Velocity–Amplitude Relationship in the Gray–Scott Autowave Model in Isolated Conditions
title_full Velocity–Amplitude Relationship in the Gray–Scott Autowave Model in Isolated Conditions
title_fullStr Velocity–Amplitude Relationship in the Gray–Scott Autowave Model in Isolated Conditions
title_full_unstemmed Velocity–Amplitude Relationship in the Gray–Scott Autowave Model in Isolated Conditions
title_short Velocity–Amplitude Relationship in the Gray–Scott Autowave Model in Isolated Conditions
title_sort velocity–amplitude relationship in the gray–scott autowave model in isolated conditions
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6740189/
https://www.ncbi.nlm.nih.gov/pubmed/31528796
http://dx.doi.org/10.1021/acsomega.9b01338
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