Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems

Advances in Applied Mathematics

Volumn 44, Issue 2, 2010, Pages 168-184

  Banaji, Murad ^a,b   Craciun, Gheorghe ^c  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF ESSEX   (United Kingdom)

^c UNIVERSITY OF WISCONSIN SCHOOL OF MEDICINE AND PUBLIC HEALTH   (United States)

Author keywords

Chemical reactions; Injectivity; Multiple equilibria; Network structure; SR graph

Indexed keywords

CHEMICAL KINETICS; CHEMICAL REACTION SYSTEMS; GENERAL CHEMICALS; GRAPH-THEORETIC; INJECTIVITY; LINEAR-ALGEBRAIC; MASS ACTION KINETICS; MICHAELIS-MENTEN KINETIC; MULTIPLE EQUILIBRIUM; NETWORK STRUCTURE; NETWORK STRUCTURES; PARAMETER VALUES; REACTION SYSTEM;

GRAFTING (CHEMICAL); NEWTONIAN FLOW; RATE CONSTANTS; SYNTHESIS (CHEMICAL);

REACTION KINETICS;

EID: 72049099058     PISSN: 01968858     EISSN: 10902074     Source Type: Journal    
DOI: 10.1016/j.aam.2009.07.003     Document Type: Article

References (15)

1. Banaji M. Monotonicity in chemical reaction systems. Dyn. Syst. 24 1 (2009) 1-30
2. M. Banaji, G. Craciun, Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements, Commun. Math. Sci., in press, preprint available at http://arxiv.org/abs/0903.1190
3. Banaji M., Donnell P., and Baigent S. P matrix properties, injectivity and stability in chemical reaction systems. SIAM J. Appl. Math. 67 6 (2007) 1523-1547
4. Brualdi R.A., and Shader B.L. Matrices of Sign-Solvable Linear Systems. Cambridge Tracts in Math. vol. 116 (1995), Cambridge University Press
5. Craciun G., and Feinberg M. Multiple equilibria in complex chemical reaction networks: I. The injectivity property. SIAM J. Appl. Math. 65 5 (2005) 1526-1546
6. Craciun G., and Feinberg M. Multiple equilibria in complex chemical reaction networks: Extensions to entrapped species models. IEEE Proc. Syst. Biol. 153 4 (2006) 179-186
7. Craciun G., and Feinberg M. Multiple equilibria in complex chemical reaction networks: II. The species-reaction graph. SIAM J. Appl. Math. 66 4 (2006) 1321-1338
8. Craciun G., Tang Y., and Feinberg M. Understanding bistability in complex enzyme-driven reaction networks. Proc. Natl. Acad. Sci. USA 103 23 (2006) 8697-8702
9. De Leenheer P., Angeli D., and Sontag E. Monotone chemical reaction networks. J. Math. Chem. 41 3 (2007) 295-314
10. Feinberg M. Complex balancing in general kinetic systems. Arch. Ration. Mech. Anal. 49 3 (1972) 187-194
11. Feinberg M. Chemical reaction network structure and the stability of complex isothermal reactors, I. The deficiency zero and deficiency one theorems. Chem. Eng. Sci. 42 10 (1987) 2229-2268
12. Horn F. On a connexion between stability and graphs in chemical kinetics, I. Stability and the reaction diagram, II. Stability and the complex graph. Proc. R. Soc. Lond. Ser. A 334 (1973) 299-330
13. Horn F., and Jackson R. General mass action kinetics. Arch. Ration. Mech. Anal. 47 2 (1972) 81-116
14. Kunze H., and Siegel D. Monotonicity properties of chemical reactions with a single initial bimolecular step. J. Math. Chem. 31 4 (2002) 339-344
15. Soulé C. Graphic requirements for multistationarity. Complexus 1 (2003) 123-133