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dc.contributor.author
Kaltenbach, Hans-Michael
dc.date.accessioned
2020-10-30T13:30:54Z
dc.date.available
2020-10-30T03:44:46Z
dc.date.available
2020-10-30T13:30:54Z
dc.date.issued
2020-09-01
dc.identifier.issn
1571-0661
dc.identifier.other
10.1016/j.entcs.2020.06.005
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/448683
dc.identifier.doi
10.3929/ethz-b-000448683
dc.description.abstract
The Jacobian matrix of a dynamic system and its principal minors play a prominent role in the study of qualitative dynamics and bifurcation analysis. When interpreting the Jacobian as an adjacency matrix of an interaction graph, its principal minors reate to sets of disjoint cycles in this graph and conditions for qualitative dynamic behaviors can be inferred from its cycle structure. The Jacobian of chemical reaction systems decomposes into the product of two matrices, which allows more fine-grained analyses by studying a corresponding bipartite species-reaction graph. Several different bipartite graphs have been proposed and results on injectivity, multistationarity, and bifurcations have been derived. Here, we present a new definition of the species-reaction graph that directly connects the cycle structure with determinant expansion terms, principal minors, and the coefficients of the characteristic polynomial. It encompasses previous graph constructions as special cases. This graph has a direct relation to the interaction graph, and properties of cycles and sub-graphs can be translated in both directions. A simple equivalence relation enables simplified decomposition of determinant expansions and allows simpler and more direct proofs of previous results.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Elsevier
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Chemical reaction network
en_US
dc.subject
Determinant
en_US
dc.subject
Bipartite graph
en_US
dc.subject
Interaction graph
en_US
dc.subject
Line-graph
en_US
dc.subject
QQualitative dynamics
en_US
dc.title
A Unified View on Bipartite Species-reaction Graphs and Their Relation to Interaction Graphs and Qualitative Dynamics of Chemical Reaction Networks
en_US
dc.type
Conference Paper
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2020-08-24
ethz.book.title
Proceedings of SASB 2018, the Ninth International Workshop on Static Analysis and Systems Biology
en_US
ethz.journal.title
Electronic notes in theoretical computer science
ethz.journal.volume
350
en_US
ethz.pages.start
73
en_US
ethz.pages.end
90
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.event
9th International Workshop on Static Analysis and Systems Biology (SASB 2018)
en_US
ethz.event.location
Freiburg, Germany
en_US
ethz.event.date
August 28, 2018
en_US
ethz.identifier.wos
ethz.publication.place
Amsterdam
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02060 - Dep. Biosysteme / Dep. of Biosystems Science and Eng.::03699 - Stelling, Jörg / Stelling, Jörg
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02060 - Dep. Biosysteme / Dep. of Biosystems Science and Eng.::03699 - Stelling, Jörg / Stelling, Jörg
ethz.date.deposited
2020-10-30T03:46:24Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2020-10-30T13:31:04Z
ethz.rosetta.lastUpdated
2021-02-15T19:30:33Z
ethz.rosetta.versionExported
true
ethz.COinS
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