Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks
We describe a necessary condition for zero-eigenvalue Turing instability, i.e., Turing instability arising from a real eigenvalue changing sign from negative to positive, for general chemical reaction networks modeled with mass-action kinetics. The reaction mechanisms are represented by the spec...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2013-05-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1207 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590143165300736 |
|---|---|
| author | Maya Mincheva Gheorghe Craciun |
| author_facet | Maya Mincheva Gheorghe Craciun |
| author_sort | Maya Mincheva |
| collection | DOAJ |
| description | We describe a necessary condition for zero-eigenvalue Turing instability, i.e., Turing instability arising from a real eigenvalue changing sign from negative to positive, for general chemical reaction networks modeled with mass-action kinetics. The reaction mechanisms are represented by the species-reaction graph (SR graph), which is a bipartite graph with different nodes representing species and reactions. If the SR graph satisfies certain conditions, similar to the conditions for ruling out multiple equilibria in spatially homogeneous differential equations systems, then the corresponding mass-action reaction-diffusion system cannot exhibit zero-eigenvalue Turing instability for any parameter values.On the other hand, if the graph-theoretic condition for ruling out zero-eigenvalue Turing instability is not satisfied, then the corresponding model may display zero-eigenvalue Turing instability for some parameter values. The technique is illustrated with a model of a bifunctional enzyme. |
| format | Article |
| id | doaj-art-b71a9b4b6ca646c0a0952001a43e33b2 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-b71a9b4b6ca646c0a0952001a43e33b22025-01-24T02:26:20ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-05-011041207122610.3934/mbe.2013.10.1207Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networksMaya Mincheva0Gheorghe Craciun1Department of Mathematical Sciences, Northern Illinois University, Dekalb, IL 60115Department of Mathematical Sciences, Northern Illinois University, Dekalb, IL 60115We describe a necessary condition for zero-eigenvalue Turing instability, i.e., Turing instability arising from a real eigenvalue changing sign from negative to positive, for general chemical reaction networks modeled with mass-action kinetics. The reaction mechanisms are represented by the species-reaction graph (SR graph), which is a bipartite graph with different nodes representing species and reactions. If the SR graph satisfies certain conditions, similar to the conditions for ruling out multiple equilibria in spatially homogeneous differential equations systems, then the corresponding mass-action reaction-diffusion system cannot exhibit zero-eigenvalue Turing instability for any parameter values.On the other hand, if the graph-theoretic condition for ruling out zero-eigenvalue Turing instability is not satisfied, then the corresponding model may display zero-eigenvalue Turing instability for some parameter values. The technique is illustrated with a model of a bifunctional enzyme.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1207chemical reaction networkssr graphturing instability.reaction-diffusion systems |
| spellingShingle | Maya Mincheva Gheorghe Craciun Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks Mathematical Biosciences and Engineering chemical reaction networks sr graph turing instability. reaction-diffusion systems |
| title | Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks |
| title_full | Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks |
| title_fullStr | Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks |
| title_full_unstemmed | Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks |
| title_short | Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks |
| title_sort | graph theoretic conditions for zero eigenvalue turing instability in general chemical reaction networks |
| topic | chemical reaction networks sr graph turing instability. reaction-diffusion systems |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1207 |
| work_keys_str_mv | AT mayamincheva graphtheoreticconditionsforzeroeigenvalueturinginstabilityingeneralchemicalreactionnetworks AT gheorghecraciun graphtheoreticconditionsforzeroeigenvalueturinginstabilityingeneralchemicalreactionnetworks |