Authors

Arjan van der Schaft, Bernhard Maschke

Abstract

This paper discusses the geometric formulation of the dynamics of chemical reaction networks within the port-Hamiltonian formalism [10, 9, 6]. The basic idea dates back to the innovative work of Oster, Perselson and Katchalsky [8, 7]. The main contribution concerns the formulation of a Dirac structure based on the stoichiometric matrix, which is underlying the port-Hamiltonian formulation. Interaction with the environment is modelled through the boundary metabolites and their boundary fluxes and affinities. This allows a compositional view on chemical reaction network dynamics.

Keywords

Reaction Network; Resistive Relation; Dirac Structure; Bond Graph; Stoichiometric Matrix

Citation

BibTeX

@inbook{van_der_Schaft_2010,
  title={{A Port-Hamiltonian Formulation of Open Chemical Reaction Networks}},
  ISBN={9783642161353},
  ISSN={1610-7411},
  DOI={10.1007/978-3-642-16135-3_27},
  booktitle={{Advances in the Theory of Control, Signals and Systems with Physical Modeling}},
  publisher={Springer Berlin Heidelberg},
  author={van der Schaft, Arjan and Maschke, Bernhard},
  year={2010},
  pages={339--348}
}

Download the bib file

References

  • Couenne, F., Jallut, C., Maschke, B., Breedveld, P. C. & Tayakout, M. Bond graph modelling for chemical reactors. Mathematical and Computer Modelling of Dynamical Systems 12, 159–174 (2006) – 10.1080/13873950500068823
  • Courant, T. J. Dirac manifolds. Trans. Amer. Math. Soc. 319, 631–661 (1990) – 10.2307/2001258
  • Craciun, G. & Feinberg, M. Multiple Equilibria in Complex Chemical Reaction Networks: II. The Species-Reaction Graph. SIAM J. Appl. Math. 66, 1321–1338 (2006) – 10.1137/050634177
  • Angeli, D., De Leenheer, P. & Sontag, E. D. A Petri net approach to the study of persistence in chemical reaction networks. Mathematical Biosciences 210, 598–618 (2007) – 10.1016/j.mbs.2007.07.003
  • Eberard, D., Maschke, B. M. & van der Schaft, A. J. An extension of Hamiltonian systems to the thermodynamic phase space: Towards a geometry of nonreversible processes. Reports on Mathematical Physics 60, 175–198 (2007) – 10.1016/s0034-4877(07)00024-9
  • Modeling and Control of Complex Physical Systems; the Port-Hamiltonian Approach (2009)
  • Oster, G. F., Perelson, A. S. & Katchalsky, A. Network thermodynamics: dynamic modelling of biophysical systems. Quart. Rev. Biophys. 6, 1–134 (1973) – 10.1017/s0033583500000081
  • Oster, G. F. & Perelson, A. S. Chemical reaction dynamics. Arch. Rational Mech. Anal. 55, 230–274 (1974) – 10.1007/bf00281751
  • A.J. Schaft van der, L 2-Gain and Passivity Techniques in Nonlinear Control (1996)
  • A.J. Schaft van der, Archiv für Elektronik und Übertragungstechnik (1995)
  • van der Schaft, A. & Maschke, B. Conservation Laws and Lumped System Dynamics. Model-Based Control: 31–48 (2009) doi:10.1007/978-1-4419-0895-7_3 – 10.1007/978-1-4419-0895-7_3