P matrix properties, injectivity, and stability in chemical reaction systems

Article

Banaji, M., Donnell, P. and Baigent, S. 2007. P matrix properties, injectivity, and stability in chemical reaction systems. SIAM Journal on Applied Mathematics. 67 (6), pp. 1523-1547. https://doi.org/10.1137/060673412
TypeArticle
TitleP matrix properties, injectivity, and stability in chemical reaction systems
AuthorsBanaji, M., Donnell, P. and Baigent, S.
Abstract

In this paper we examine matrices which arise naturally as Jacobians in chemical dynamics. We are particularly interested in when these Jacobians are P matrices (up to a sign change), ensuring certain bounds on their eigenvalues, precluding certain behaviour such as multiple equilibria, and sometimes implying stability. We first explore reaction systems and derive results which provide a deep connection between system structure and the P matrix property. We then examine a class of systems consisting of reactions coupled to an external rate-dependent negative feedback process, and characterise conditions which ensure the P matrix property survives the negative feedback. The techniques presented are applied to examples published in the mathematical and biological literature.

PublisherSociety for Industrial and Applied Mathematics
JournalSIAM Journal on Applied Mathematics
ISSN0036-1399
Publication dates
Online07 Sep 2007
Publication process dates
Deposited28 Oct 2016
Accepted08 May 2007
Output statusPublished
Accepted author manuscript
Copyright Statement

This is the accepted manuscript the final article published as: SIAM Journal on Applied Mathematics, 2007, Vol. 67, No. 6 : pp. 1523-1547, P Matrix Properties, Injectivity, and Stability in Chemical Reaction Systems
Murad Banaji, Pete Donnell, and Stephen Baigent
(doi: 10.1137/060673412). Copyright © 2007 Society for Industrial and Applied Mathematics
Read More: http://epubs.siam.org/doi/10.1137/060673412

Digital Object Identifier (DOI)https://doi.org/10.1137/060673412
LanguageEnglish
Permalink -

https://repository.mdx.ac.uk/item/86v01

Log in to edit

Download files

Accepted author manuscript
Pmat1.pdf

  • 24
    total views
  • 35
    total downloads
  • 1
    views this month
  • 2
    downloads this month

Export as

Related outputs

Splitting reactions preserves nondegenerate behaviors in chemical reaction networks
Banaji, M. 2023. Splitting reactions preserves nondegenerate behaviors in chemical reaction networks. SIAM Journal on Applied Mathematics. 83 (2), pp. 748-769. https://doi.org/10.1137/22m1478392
The smallest bimolecular mass-action system with a vertical Andronov–Hopf bifurcation
Banaji, M., Boros, B. and Hofbauer, J. 2023. The smallest bimolecular mass-action system with a vertical Andronov–Hopf bifurcation. Applied Mathematics Letters. 143. https://doi.org/10.1016/j.aml.2023.108671
The smallest bimolecular mass action reaction networks admitting Andronov–Hopf bifurcation
Banaji, M. and Boros, B. 2023. The smallest bimolecular mass action reaction networks admitting Andronov–Hopf bifurcation. Nonlinearity. 36 (2), pp. 1398-1433. https://doi.org/10.1088/1361-6544/acb0a8
Estimates of pandemic excess mortality in India based on civil registration data
Banaji, M. and Gupta, A. 2022. Estimates of pandemic excess mortality in India based on civil registration data. PLOS Global Public Health. 2 (12), pp. 1-17. https://doi.org/10.1371/journal.pgph.0000803
Inheritance of oscillation in chemical reaction networks
Banaji, M. 2018. Inheritance of oscillation in chemical reaction networks. Applied Mathematics and Computation. 325, pp. 191-209. https://doi.org/10.1016/j.amc.2017.12.012
The inheritance of nondegenerate multistationarity in chemical reaction networks
Banaji, M. and Pantea, C. 2018. The inheritance of nondegenerate multistationarity in chemical reaction networks. SIAM Journal on Applied Mathematics. 78 (2), pp. 1105-1130. https://doi.org/10.1137/16M1103506
Cycle structure in SR and DSR graphs: implications for multiple equilibria and stable oscillation in chemical reaction networks
Banaji, M. 2012. Cycle structure in SR and DSR graphs: implications for multiple equilibria and stable oscillation in chemical reaction networks. in: Jensen, K., Donatelli, S. and Kleijn, J. (ed.) Transactions on Petri Nets and Other Models of Concurrency V Springer Berlin. Heidelberg.
Monotonicity in chemical reaction systems
Banaji, M. 2009. Monotonicity in chemical reaction systems. Dynamical Systems. 24 (1), pp. 1-30. https://doi.org/10.1080/14689360802243813
Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems
Banaji, M. and Craciun, G. 2009. Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems. Advances in Applied Mathematics. 44 (2), pp. 168-184. https://doi.org/10.1016/j.aam.2009.07.003
Graph-theoretic conditions for injectivity of functions on rectangular domains
Banaji, M. 2010. Graph-theoretic conditions for injectivity of functions on rectangular domains. Journal of Mathematical Analysis and Applications. 370 (1), pp. 302-311. https://doi.org/10.1016/j.jmaa.2010.04.078
P-matrices and signed digraphs
Banaji, M. and Rutherford, C. 2010. P-matrices and signed digraphs. Discrete Mathematics. 311 (4), pp. 295-301. https://doi.org/10.1016/j.disc.2010.10.018
Global convergence in systems of differential equations arising from chemical reaction networks
Banaji, M. and Mierczyński, J. 2012. Global convergence in systems of differential equations arising from chemical reaction networks. Journal of Differential Equations. 254 (3), pp. 1359-1374. https://doi.org/10.1016/j.jde.2012.10.018
A graph-theoretic condition for irreducibility of a set of cone preserving matrices
Banaji, M. and Burbanks, A. 2013. A graph-theoretic condition for irreducibility of a set of cone preserving matrices. Linear Algebra and its Applications. 438 (11), pp. 4103-4113. https://doi.org/10.1016/j.laa.2013.01.029
Local and global stability of equilibria for a class of chemical reaction networks
Donnell, P. and Banaji, M. 2013. Local and global stability of equilibria for a class of chemical reaction networks. SIAM Journal on Applied Dynamical Systems. 12 (2), pp. 899-920. https://doi.org/10.1137/120898486
Combinatorial approaches to Hopf bifurcations in systems of interacting elements
Angeli, D., Banaji, M. and Pantea, C. 2013. Combinatorial approaches to Hopf bifurcations in systems of interacting elements. Communications in Mathematical Sciences. 12 (6), pp. 1101-1133.
Some results on the structure and spectra of matrix-products
Banaji, M. and Rutherford, C. 2015. Some results on the structure and spectra of matrix-products. Linear Algebra and its Applications. 474, pp. 192-212. https://doi.org/10.1016/j.laa.2015.02.008
Some results on injectivity and multistationarity in chemical reaction networks
Banaji, M. and Pantea, C. 2016. Some results on injectivity and multistationarity in chemical reaction networks. SIAM Journal on Applied Dynamical Systems. 15 (2), pp. 807-869. https://doi.org/10.1137/15M1034441