Please use this identifier to cite or link to this item: http://doi.org/10.25358/openscience-7239
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dc.contributor.authorBrechmann, Pia-
dc.contributor.authorRendall, Alan D.-
dc.date.accessioned2022-06-28T10:03:22Z-
dc.date.available2022-06-28T10:03:22Z-
dc.date.issued2021-
dc.identifier.urihttps://openscience.ub.uni-mainz.de/handle/20.500.12030/7253-
dc.description.abstractThe Selkov oscillator, a simple description of glycolysis, is a system of two ordinary differential equations with mass action kinetics. In previous work the authors established several properties of the solutions of this system. In the present paper we extend this to prove that this system has solutions which diverge to infinity in an oscillatory manner at late times. This is done with the help of a Poincaré compactification of the system and a shooting argument. This system was originally derived from another system with Michaelis–Menten kinetics. A Poincaré compactification of the latter system is carried out and this is used to show that the Michaelis–Menten system, like that with mass action, has solutions which diverge to infinity in a monotone manner. It is also shown to admit subcritical Hopf bifurcations and thus unstable periodic solutions. We discuss to what extent the unbounded solutions cast doubt on the biological relevance of the Selkov oscillator and compare it with other models for the same biological system in the literature.en_GB
dc.language.isoengde
dc.rightsCC BY*
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/*
dc.subject.ddc510 Mathematikde_DE
dc.subject.ddc510 Mathematicsen_GB
dc.titleUnbounded solutions of models for glycolysisen_GB
dc.typeZeitschriftenaufsatzde
dc.identifier.doihttp://doi.org/10.25358/openscience-7239-
jgu.type.dinitypearticleen_GB
jgu.type.versionPublished versionde
jgu.type.resourceTextde
jgu.organisation.departmentFB 08 Physik, Mathematik u. Informatikde
jgu.organisation.number7940-
jgu.organisation.nameJohannes Gutenberg-Universität Mainz-
jgu.rights.accessrightsopenAccess-
jgu.journal.titleJournal of mathematical biologyde
jgu.journal.volume82de
jgu.pages.alternative1de
jgu.publisher.year2021-
jgu.publisher.nameSpringerde
jgu.publisher.placeBerlin u.a.de
jgu.publisher.issn1432-1416de
jgu.organisation.placeMainz-
jgu.subject.ddccode510de
jgu.publisher.doi10.1007/s00285-021-01560-yde
jgu.organisation.rorhttps://ror.org/023b0x485
Appears in collections:JGU-Publikationen

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