Skip to main content
SpringerLink
Log in

The existence and uniqueness of steady states for a class of chemical reaction networks

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Edelstein, B., 1970, A biochemical model with multiple steady states and hysteresis, J. Theor. Biol. 29, 57–62.

    Google Scholar 

  2. Feinberg, M., 1972, Complex balancing in general kinetic systems, Arch. Rational Mech. Anal., 49, 187–194.

    Google Scholar 

  3. Feinberg, M., 1977, Mathematical aspects of mass action kinetics, Chemical Reactor Theory: A Review, eds. L. Lapidus & N. Amundson, Prentice-Hall, Englewood Cliffs, N.J., 1–78.

    Google Scholar 

  4. Feinberg, M., 1980, Chemical oscillations, multiple equilibria and reaction network structure, Dynamics and Modelling of Reactive Systems, eds. W. Stewart, W. H. Ray & C. Conley, Academic Press, New York, 59–130.

    Google Scholar 

  5. Feinberg, M., 1987, Chemical reaction network structure and the stability of complex isothermal reactors I. The deficiency zero and deficiency one theorems, Chemical Engineering Science, 42, 2229–2268.

    Google Scholar 

  6. Feinberg, M., 1988, Chemical reaction network structure and the stability of complex isothermal reactors II. Multiple steady states for networks of deficiency one, Chemical Engineering Science, 43, 1–25.

    Google Scholar 

  7. Feinberg, M., 1995, Multiple steady states for chemical reaction networks of deficiency one, Arch. Rational Mech. Anal., 132, 371–406

    Google Scholar 

  8. Feinberg, M. & F. J. M. Horn, 1974, Dynamics of open chemical systems and the algebraic structure of the underlying reaction network, Chemical Engineering Science, 29, 775–787.

    Google Scholar 

  9. Feinberg, M. & F. J. M. Horn, 1977, Chemical mechanism structure and the coincidence of the stoichiometric and kinetic subspaces, Arch. Rational Mech. Anal., 66, 83–97.

    Google Scholar 

  10. Horn, F. J. M. & R. Jackson, 1972, General mass action kinetics, Arch. Rational Mech. Anal., 47, 81–116.

    Google Scholar 

  11. Horn, F. J. M., 1972, Necessary and sufficient conditions for complex balancing in chemical kinetics, Arch. Rational Mech. Anal., 49, 172–186.

    Google Scholar 

  12. Hirsch, M. W. & S. Smale, 1974, Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, New York.

    Google Scholar 

  13. Stoer, J. & C. Witzgall, 1970, Convexity and Optimization in Finite Dimensions, Springer-Verlag, Berlin-Heidelberg-New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, University of Rochester, 14627, Rochester, New York

    Martin Feinberg

Authors
  1. Martin Feinberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by the Editor

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feinberg, M. The existence and uniqueness of steady states for a class of chemical reaction networks. Arch. Rational Mech. Anal. 132, 311–370 (1995). https://doi.org/10.1007/BF00375614

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00375614

Keywords

Search

Navigation