In [1] we have discussed a mathematical model of finitely many cells Zj (j =1,…,N) (see fig.1) in which a chemical reaction occurs. A membrane M.j+1 between Zj and Zj+1 allows for diffusive and/or convective transport. We have shown that branches of stable steady states are possible involving alterations of substrate concentration in Z1 and ZN only whereas Z2,…,ZN-1 operate on a nearly constant concentration level along the branch. There are symmetric and unsymmetric steady states of this kind (see also section 2).


Hysteresis Loop Cell Model Bifurcation Diagram Bifurcation Point Full System 
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  1. 1.
    Bigge, J., Bohl, E. (1982) On the steady states of finitely many chemical cells. Submitted for publication.Google Scholar
  2. 2.
    Bohl, E. (1981) Finite Modelle gewöhnlicher Randwertaufgaben. (Teubner, Stuttgart).Google Scholar
  3. 3.
    Kernevez, J.-P., Thomas, D. (1975) Numerical analysis of some biochemical systems. Appl. Math. Optim. 1, 222–285.CrossRefGoogle Scholar
  4. 4.
    Murray, J.D. (1977) Lectures on nonlinear-differential-equation models in biologie. (Oxford).Google Scholar

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© Springer Basel AG 1983

Authors and Affiliations

  • Erich Bohl
    • 1
  1. 1.Fakultät für MathematikUniversität KonstanzKonstanzFederal Republic of Germany

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