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All issues Volume 10 / No 5 (2015) Math. Model. Nat. Phenom., 10 5 (2015) 47-67 References
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Issue
Math. Model. Nat. Phenom.
Volume 10, Number 5, 2015
Dynamics of Chemical Reaction Networks
Page(s) 47 - 67
DOI https://doi.org/10.1051/mmnp/201510504
Published online 27 August 2015
  1. D. Angeli, P. De Leenheer, E. Sontag. Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates. J. Math. Biol., 61 (2010), no. 4, 581–616. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  2. M. Banaji. Monotonicity in chemical reaction systems. Dyn. Syst., 24 (2009), no. 1, 1–30. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Banaji, G. Craciun. Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems. Adv. Appl. Math., 44 (2010), no. 2, 168–184. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  4. M. Banaji, J. Mierczyński. Global convergence in systems of differential equations arising from chemical reaction networks. J. Differential Equations, 254 (2013), no. 3, 1359–1374. [CrossRef] [MathSciNet] [Google Scholar]
  5. M. Banaji, C. Pantea. Some results on injectivity and multistationarity in chemical reaction networks. preprint, http://arXiv.org/abs/1309.6771, (2013). [Google Scholar]
  6. C. Conradi, D. Flockerzi, J. Raisch, J. Stelling. Subnetwork analysis reveals dynamic features of complex (bio)chemical networks. Proc. Natl. Acad. Sci. USA, 104 (2007), no. 49, 19175–19180. [CrossRef] [Google Scholar]
  7. C. Conradi, M. Mincheva. Graph-theoretic analysis of multistationarity using degree theory. preprint, http://arxiv.org/abs/1411.2896, (2014). [Google Scholar]
  8. G. Craciun, M. Feinberg. Multiple equilibria in complex chemical reaction networks. I. The injectivity property. SIAM J. Appl. Math., 65 (2005), no. 5, 1526–1546. [CrossRef] [Google Scholar]
  9. G. Craciun, M. Feinberg. Multiple equilibria in complex chemical reaction networks: extensions to entrapped species models. IEE Proceedings-Systems Biology, 153 (2006), 179–186. [CrossRef] [Google Scholar]
  10. G. Craciun, M. Feinberg. Multiple equilibria in complex chemical reaction networks. II. The species-reaction graph. SIAM J. Appl. Math., 66 (2006), no. 4, 1321–1338. [CrossRef] [Google Scholar]
  11. G. Craciun, M. Feinberg. Multiple equilibria in complex chemical reaction networks: Semiopen mass action systems. SIAM J. Appl. Math., 70 (2010), no. 6, 1859–1877. [CrossRef] [Google Scholar]
  12. G. Craciun, L. Garcia-Puente, F. Sottile. Some geometrical aspects of control points for toric patches. In M. Dæhlen, M. S. Floater, T. Lyche, J.-L. Merrien, K. Morken, L. L. Schumaker, eds., Mathematical Methods for Curves and Surfaces, vol. 5862 of Lecture Notes in Comput. Sci., pages 111–135. Springer, Heidelberg, 2010. [Google Scholar]
  13. G. Craciun, C. Pantea, E. Sontag. Graph-theoretic characterizations of multistability and monotonicity for biochemical reaction networks, pages 63–72. Springer, 2011. [Google Scholar]
  14. P. Donnell, M. Banaji. Local and global stability of equilibria for a class of chemical reaction networks. SIAM J. Appl. Dyn. Syst., 12 (2013), no. 2, 899–920. [CrossRef] [Google Scholar]
  15. P. Donnell, M. Banaji, A. Marginean, C. Pantea. CoNtRol: an open source framework for the analysis of chemical reaction networks. Bioinformatics, (2014), to appear. [Google Scholar]
  16. P. Ellison. The advanced deficiency algorithm and its applications to mechanism discrimination. Ph.D. thesis, University of Rochester, 1998. [Google Scholar]
  17. P. Ellison, M. Feinberg, H. Ji, D. Knight. Chemical Reaction Network Toolbox, 2011. Available at http://www.crnt.osu.edu/CRNTWin. [Google Scholar]
  18. M. Feinberg. Complex balancing in general kinetic systems. Arch. Rational Mech. Anal., 49 (1972), no. 3, 187–194. [Google Scholar]
  19. M. Feinberg. Chemical reaction network structure and the stability of complex isothermal reactors I. The deficiency zero and deficiency one theorems. Chem. Eng. Sci., 42 (1987), no. 10, 2229–2268. [Google Scholar]
  20. M. Feinberg. Multiple steady states for chemical reaction networks of deficiency one. Arch. Rational Mech. Anal., 132 (1995), no. 4, 371–406. [CrossRef] [MathSciNet] [Google Scholar]
  21. E. Feliu. Injectivity, multiple zeros, and multistationarity in reaction networks. preprint, http://arXiv.org/abs/1407.2955, (2014). [Google Scholar]
  22. E. Feliu, C. Wiuf. Preclusion of switch behavior in reaction networks with mass-action kinetics. Appl. Math. Comput., 219 (2012), 1449–1467. [CrossRef] [Google Scholar]
  23. E. Feliu, C. Wiuf. Simplifying biochemical models with intermediate species. J. R. Soc. Interface, 10 (2013), no. 87. [Google Scholar]
  24. D. Fouchet, R. Regoes. A population dynamics analysis of the interaction between adaptive regulatory T cells and antigen presenting cells. PLoS ONE, 3 (2008), no. 5, e2306. [CrossRef] [PubMed] [Google Scholar]
  25. G. Gnacadja. A Jacobian criterion for the simultaneous injectivity on positive variables of linearly parameterized polynomials maps. Linear Algebra Appl., 437 (2012), 612–622. [CrossRef] [Google Scholar]
  26. P. Grassberger. On phase transitions in Schlögl’s second model. Zeitschrift für Physik B Condensed Matter, 47 (1982), no. 4, 365–374. [Google Scholar]
  27. J. W. Helton, I. Klep, R. Gomez. Determinant expansions of signed matrices and of certain Jacobians. SIAM J. Matrix Anal. Appl., 31 (2009), no. 2, 732–754. [CrossRef] [MathSciNet] [Google Scholar]
  28. A. Ivanova. Conditions for uniqueness of stationary state of kinetic systems related to structural scheme of reactions. Kinet. Katal., 20 (1979), 1019–1023. [Google Scholar]
  29. H. Ji. Uniqueness of Equilibria for Complex Chemical Reaction Networks. Ph.D. thesis, Ohio State University, 2011. [Google Scholar]
  30. B. Joshi. Complete characterization by multistationarity of fully open networks with one non-flow reaction. Applied Mathematics and Computation, 219 (2013), 6931–6945. [CrossRef] [Google Scholar]
  31. B. Joshi, A. Shiu. Simplifying the Jacobian criterion for precluding multistationarity in chemical reaction networks. SIAM J. Appl. Math., 72 (2012), no. 3, 857–876. [CrossRef] [Google Scholar]
  32. B. Joshi, A. Shiu. Atoms of multistationarity in chemical reaction networks. Journal of Mathematical Chemistry, 51 (2013), no. 1, 153–178. [Google Scholar]
  33. K. P. Lesch, D. Bengel. Neurotransmitter reuptake mechanisms. CNS drugs, 4 (1995), no. 4, 302–322. [CrossRef] [Google Scholar]
  34. G. Marin, G. S. Yablonsky. Kinetics of Chemical Reactions. Wiley-VCH, Wienheim, Germany, 2011. [Google Scholar]
  35. M. Mincheva, G. Craciun. Multigraph conditions for multistability, oscillations and pattern formation in biochemical reaction networks. Proceedings of the IEEE, 96 (2008), no. 8, 1281–1291. [CrossRef] [Google Scholar]
  36. S. Müller, E. Feliu, G. Regensburger, C. Conradi, A. Shiu, A. Dickenstein. Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry. to appear in Found. Comput. Math. [Google Scholar]
  37. M. Santillán, M. C. Mackey. Dynamic regulation of the tryptophan operon: a modeling study and comparison with experimental data. Proceedings of the National Academy of Sciences, 98 (2001), no. 4, 1364–1369. [CrossRef] [Google Scholar]
  38. F. Schlögl. Chemical reaction models for non-equilibrium phase transitions. Zeitschrift für Physik, 253 (1972), no. 2, 147–161. [Google Scholar]
  39. P. M. Schlosser, M. Feinberg. A theory of multiple steady states in isothermal homogeneous CFSTRs with many reactions. Chemical Engineering Science, 49 (1994), no. 11, 1749–1767. [CrossRef] [Google Scholar]
  40. G. Shinar, M. Feinberg. Concordant chemical reaction networks. Math. Biosci., 240 (2012), no. 2, 92–113. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  41. G. Shinar, M. Feinberg. Concordant chemical reaction networks and the species-reaction graph. Math. Biosci., 241 (2013), no. 1, 1–23. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  42. D. Siegal-Gaskins, M. K. Mejia-Guerra, G. D. Smith, E. Grotewold. Emergence of switch-like behavior in a large family of simple biochemical networks. PLoS Comput. Biol., 7 (2011), no. 5, e1002039. [CrossRef] [Google Scholar]
  43. C. Wiuf, E. Feliu. Power-law kinetics and determinant criteria for the preclusion of multistationarity in networks of interacting species. SIAM J. Appl. Dyn. Syst., 12 (2013), 1685–1721. [CrossRef] [Google Scholar]
  44. G. Yablonskii, V. Bykov, A. Gorban, V. Elokhin. Kinetic Models of Catalytic Reactions. Comprehensive Chemical Kinetics, vol. 32, ed. by R.G. Compton, Elsevier, Amsterdam, 1991. [Google Scholar]

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