Weakly reversible mass-Action systems with infinitely many positive steady states

Balazs Boros; Gheorghe Craciun; Polly Y. Yu

doi:10.1137/19m1303034

Weakly reversible mass-Action systems with infinitely many positive steady states

Balazs Boros
, Gheorghe Craciun
, Polly Y. Yu

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

Abstract

We show that weakly reversible mass-Action systems can have a continuum of positive steady states, coming from the zeroes of a multivariate polynomial. Moreover, the same is true of systems whose underlying reaction network is reversible and has a single connected component. In our construction, we relate operations on the reaction network to the multivariate polynomial occurring as a common factor in the system of differential equations.

Original language	English (US)
Pages (from-to)	1936-1946
Number of pages	11
Journal	SIAM Journal on Applied Mathematics
Volume	80
Issue number	4
DOIs	https://doi.org/10.1137/19m1303034
State	Published - 2020
Externally published	Yes

Keywords

Mass-Action system
Positive steady states
Reaction network
Weak reversibility

ASJC Scopus subject areas

Applied Mathematics

Online availability

10.1137/19m1303034

Library availability

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title = "Weakly reversible mass-Action systems with infinitely many positive steady states",

abstract = "We show that weakly reversible mass-Action systems can have a continuum of positive steady states, coming from the zeroes of a multivariate polynomial. Moreover, the same is true of systems whose underlying reaction network is reversible and has a single connected component. In our construction, we relate operations on the reaction network to the multivariate polynomial occurring as a common factor in the system of differential equations.",

keywords = "Mass-Action system, Positive steady states, Reaction network, Weak reversibility",

author = "Balazs Boros and Gheorghe Craciun and Yu, \{Polly Y.\}",

note = "\textbackslash{}ast Received by the editors December 23, 2019; accepted for publication (in revised form) April 27, 2020; published electronically August 27, 2020. https://doi.org/10.1137/19M1303034 Funding: The work of the first author was supported by the Austrian Science Fund (FWF) through project P28406. The work of the second and third authors was partially supported by the National Science Foundation (NSF) under grant DMS-1816238. The work of the third author was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) PGS-D. \textbackslash{}dagger Department of Mathematics, University of Wisconsin--Madison, Madison, WI 53706 ([email protected], [email protected]). \textbackslash{}ddagger Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin--Madison, Madison, WI 53706 ([email protected]).",

year = "2020",

doi = "10.1137/19m1303034",

language = "English (US)",

volume = "80",

pages = "1936--1946",

journal = "SIAM Journal on Applied Mathematics",

issn = "0036-1399",

publisher = "Society for Industrial and Applied Mathematics Publications",

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TY - JOUR

T1 - Weakly reversible mass-Action systems with infinitely many positive steady states

AU - Boros, Balazs

AU - Craciun, Gheorghe

AU - Yu, Polly Y.

N1 - \ast Received by the editors December 23, 2019; accepted for publication (in revised form) April 27, 2020; published electronically August 27, 2020. https://doi.org/10.1137/19M1303034 Funding: The work of the first author was supported by the Austrian Science Fund (FWF) through project P28406. The work of the second and third authors was partially supported by the National Science Foundation (NSF) under grant DMS-1816238. The work of the third author was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) PGS-D. \dagger Department of Mathematics, University of Wisconsin--Madison, Madison, WI 53706 ([email protected], [email protected]). \ddagger Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin--Madison, Madison, WI 53706 ([email protected]).

PY - 2020

Y1 - 2020

N2 - We show that weakly reversible mass-Action systems can have a continuum of positive steady states, coming from the zeroes of a multivariate polynomial. Moreover, the same is true of systems whose underlying reaction network is reversible and has a single connected component. In our construction, we relate operations on the reaction network to the multivariate polynomial occurring as a common factor in the system of differential equations.

AB - We show that weakly reversible mass-Action systems can have a continuum of positive steady states, coming from the zeroes of a multivariate polynomial. Moreover, the same is true of systems whose underlying reaction network is reversible and has a single connected component. In our construction, we relate operations on the reaction network to the multivariate polynomial occurring as a common factor in the system of differential equations.

KW - Mass-Action system

KW - Positive steady states

KW - Reaction network

KW - Weak reversibility

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UR - https://www.scopus.com/pages/publications/85098438896#tab=citedBy

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DO - 10.1137/19m1303034

M3 - Article

AN - SCOPUS:85098438896

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VL - 80

SP - 1936

EP - 1946

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 4

ER -

Weakly reversible mass-Action systems with infinitely many positive steady states

Abstract

Keywords

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