Free Access
Issue
Math. Model. Nat. Phenom.
Volume 10, Number 5, 2015
Dynamics of Chemical Reaction Networks
Page(s) 84 - 99
DOI https://doi.org/10.1051/mmnp/201510506
Published online 27 August 2015
  1. E. Akin. The Geometry of Population Genetics, vol. 31 of Lect. Notes in Biomath., Springer, New York, 1979. [Google Scholar]
  2. E. Baake. Deterministic and stochastic aspects of single-crossover recombination, in Proceedings of the International Congress of Mathematicians. Volume IV, Hindustan Book Agency, New Delhi, 2010, pp. 3037–3053. [Google Scholar]
  3. R. Bürger. The Mathematical Theory of Selection, Recombination, and Mutation, John Wiley & Sons, 2000. [Google Scholar]
  4. A. Dickenstein, M. Pérez Millán. How far is complex balancing from detailed balancing?, Bull. Math. Biol., 73 (2011), pp. 811–828. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  5. M. Feinberg. Necessary and sufficient conditions for detailed balancing in mass action systems of arbitrary complexity, Chemical Engineering Science, 44 (1989), pp. 1819–1827. [CrossRef] [Google Scholar]
  6. M. Feinberg. The existence and uniqueness of steady states for a class of chemical reaction networks, Arch. Rational Mech. Anal., 132 (1995), pp. 311–370. [CrossRef] [MathSciNet] [Google Scholar]
  7. H. Geiringer. On the probability theory of linkage in Mendelian heredity, Annals Math. Statist., 15 (1944), pp. 25–57. [CrossRef] [Google Scholar]
  8. A. N. Gorban. General H-theorem and entropies that violate the second law, Entropy, 16 (2014), pp. 2408–2432. [CrossRef] [MathSciNet] [Google Scholar]
  9. J. Higgins. Some remarks on Shear’s Liapunov function for systems of chemical reactions, Journal of Theoretical Biology, 21 (1968), pp. 293–304. [CrossRef] [PubMed] [Google Scholar]
  10. F. Horn. Necessary and sufficient conditions for complex balancing in chemical kinetics, Arch. Rational Mech. Anal., 49 (1972), pp. 172–186. [Google Scholar]
  11. F. Horn, R. Jackson. General mass action kinetics, Arch. Ration. Mech. Anal., 47 (1972), pp. 81–116. [CrossRef] [Google Scholar]
  12. L. A. Kun, Y. I. Lyubich. The H-theorem and convergence to equilibrium for free multi-locus populations, Kibernetika, (1980), p. 150. [Google Scholar]
  13. Y. I. Lyubich. Mathematical Structures in Population Genetics, vol. 22 of Biomathematics, Springer-Verlag, Berlin, 1992. Translated from the 1983 Russian original by D. Vulis and A. Karpov. [Google Scholar]
  14. L. Markus. Asymptotically autonomous differential systems, in Contributions to the theory of nonlinear oscillations, vol. 3, vol. 36 of Annals of Mathematics Studies, Princeton University Press, 1956, pp. 17–29. [Google Scholar]
  15. K. Mischaikow, H. Smith, H. R. Thieme. Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions, Trans. Amer. Math. Soc., 347 (1995), pp. 1669–1685. [CrossRef] [MathSciNet] [Google Scholar]
  16. S. Müller, G. Regensburger. Generalized mass-action systems and positive solutions of polynomial equations with real and symbolic exponents (invited talk), in Computer Algebra in Scientific Computing, V. P. Gerdt, W. Koepf, W. Seiler, and E. V. Vorozhtsov, eds., vol. 8660 of Lecture Notes in Computer Science, Springer International Publishing, 2014, pp. 302–323. [Google Scholar]
  17. T. Nagylaki. The evolution of multilocus systems under weak selection, Genetics, 134 (1993), pp. 627–47. [PubMed] [Google Scholar]
  18. T. Nagylaki, J. Hofbauer, P. Brunovský. Convergence of multilocus systems under weak epistasis or weak selection, Journal of Mathematical Biology, 38 (1999), pp. 103–133. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  19. S. Shahshahani. A new mathematical framework for the study of linkage and selection, vol. 211 of Memoirs of the AMS, Amer. Math. Soc., 1979. [Google Scholar]
  20. D. Siegel, D. MacLean. Global stability of complex balanced mechanisms, J. Math. Chemistry, 27 (2000), pp. 89–110. [CrossRef] [Google Scholar]
  21. V. M. Vasil’ev, A. I. Vol’pert, S. I. Hudjaev. The method of quasi-stationary concentrations for the equations of chemical kinetics, Comput. Math. Math. Phys., 13 (1974), pp. 187–206. [CrossRef] [Google Scholar]
  22. A. I. Vol’pert, S. I. Hudjaev. Analysis in classes of discontinuous functions and equations of mathematical physics, vol. 8 of Mechanics: Analysis, Martinus Nijhoff Publishers, Dordrecht, 1985. [Google Scholar]
  23. R. Wegscheider. Über simultane Gleichgewichte und die Beziehungen zwischen Thermodynamik und Reactionskinetik homogener Systeme, Monatshefte für Chemie und verwandte Teile anderer Wissenschaften, 22 (1901), pp. 849–906. [CrossRef] [Google Scholar]
  24. Y. B. Zel’dovich. The proof of uniqueness of the solution of mass law equations, Zhurnal fizicheskoi khimii, 11 (1938), pp. 685–687. [Google Scholar]

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