Free Access
Issue
Math. Model. Nat. Phenom.
Volume 10, Number 5, 2015
Dynamics of Chemical Reaction Networks
Page(s) 100 - 118
DOI https://doi.org/10.1051/mmnp/201510507
Published online 27 August 2015
  1. D. Bartel. MicroRNAs: target recognition and regulatory functions. Cell, 136 (2009), 215–233. [CrossRef] [PubMed] [Google Scholar]
  2. T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein. Introduction to Algorithms. MIT Press, 2nd edition, 2001. [Google Scholar]
  3. E. N. Dancer, P. Poláčik. Realization of vector fields and dynamics of spatially homogeneous parabolic equations. Memoirs of Amer. Math. Society, 140 (668) (1999). [CrossRef] [Google Scholar]
  4. H. Errami, W. M. Seiler, M. Eiswirth, A. Weber. Computing Hopf bifurcations in chemical reaction networks using reaction coordinates. In V. P. Gerdt, W. Koepf, E. W. Mayr, E. V. Vorozhtsov, editors, Computer Algebra in Scientific Computing, volume 7442 of Lecture Notes in Computer Science, pages 84–97. Springer, Berlin–Heidelberg, 2012. [Google Scholar]
  5. M. Gary, D. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. W. H. Freeman, New York, 1979. [Google Scholar]
  6. K. Gatermann, M. Eiswirth, A. Sensse. Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems. Journal of Symbolic Computation, 40 (6) (2005), 1361–1382. [CrossRef] [MathSciNet] [Google Scholar]
  7. H. Haken. Synergetics—An Introduction. Springer, Berlin, 3rd edition, 1983. [Google Scholar]
  8. A. Halmschlager, L. Szenthe, J. Tóth. Neural networks and physical systems with emergent collective computational abilities. Electronic Journal of Qualitative Theory of Differential Equations, 14 (2004), 1–14. [Google Scholar]
  9. D. Heitzler, G. Durand, N. Gallay, A. Rizk, S. Ahn, J. Kim, J. D. Violin, L. Dupuy, C. Gauthier, V. Piketty, P. Crépieux, A. Poupon, F. Clément, F. Fages, R. J. Lefkowitz, E. Reiter. Competing G protein-coupled receptor kinases balance G protein and β-arrestin signaling. Molecular systems biology, 8 (590) (2012), 590. [CrossRef] [PubMed] [Google Scholar]
  10. D. Henry, D. B. Henry. Geometric theory of semilinear parabolic equations. Lecture Notes in Mathematics. Springer, Berlin, 1981. [Google Scholar]
  11. H. Jeong, B. Tombor, R. Albert, Z. Oltvai, A. Barabási. The large-scale organization of metabolic networks. Nature, 407 (2000), 641–654. [Google Scholar]
  12. M. D. Korzuchin. Kolebaltelnie processi v biologicheskih i chimicheskih sistemach. Thesis. 231 pp. Moscow, 1967. In Russian. [Google Scholar]
  13. N. V. Kuznetsov, G. A. Leonov. Lyapunov quantities and limit cycles of two-dimensional dynamical systems. In Dynamics and Control of Hybrid Mechanical Systems, pp. 7–28. World Scientific, 2010. [Google Scholar]
  14. A. L. Lehninger, D. L. Nelson, M. M. Cox. Principles of Biochemistry. Worth, New York, 2nd edition, 1993. [Google Scholar]
  15. A. Lesne. Complex networks: from graph theory to biology. Lett. Math. Phys., 78 (2006), 235–262. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  16. D. Ruelle, F. Takens. Elements of differentiable dynamics and bifurcation theory. Academic Press, Boston, 1989. [Google Scholar]
  17. S. S. Samal, H. Errami, A. Weber. PoCaB: a software infrastructure to explore algebraic methods for bio-chemical reaction networks. In V. P. Gerdt, W. Koepf, E. W. Mayr, E. V. Vorozhtsov, editors, Computer Algebra in Scientific Computing, volume 7442 of Lecture Notes in Computer Science, pp. 294–307. Springer, Berlin–Heidelberg, 2012. [Google Scholar]
  18. Y. Shimoni, G. Friedlander, G. Hetzroni. Regulation of gene expression by small non-coding RNAs: a quantitative view. Molecular Systems Biology, 3 (1) (2007), 138. [CrossRef] [PubMed] [Google Scholar]
  19. A. M. Zhabotinsky. Konzentrazionnie avtokolebania. Nauka, Moscow, 1974. in Russian. [Google Scholar]
  20. J. Zhao, H. Yu, J. Luo, Z. W. Cao, Y. X. Li. Hierarchical modularity of nested bow-ties in metabolic networks. BMC bioinformatics, 7 (2006), 386 [CrossRef] [PubMed] [Google Scholar]
  21. V. Zhdanov. Kinetic models of gene expression including non-coding RNAs. Physics Reports, 500 (1) (2011), 1–42. [CrossRef] [Google Scholar]
  22. Conradi, C., Flockerzi, D., & Raisch, J. (2008). Multistationarity in the activation of a MAPK: parametrizing the relevant region in parameter space. Mathematical biosciences, 211(1), 105-31, doi:10.1016/j.mbs.2007.10.004. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]

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