Skip to main content
SpringerLink
Log in

Interactions among biological systems: An analysis of asymptotic stability

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

An analysis of the interactions among asymptotically stable dynamical systems is formulated by making use of the dynamical system theory. Some results coming from previous mathematical analyses have been slightly modified to take into account some typical biological constraints as the boundedness properties of the solutions. In particular it has been shown that when the “coupling” among the subsystems is “loose” enough (in a sense that has to be made mathematically precise) the asymptotic behaviour of a complex system is the same of that of its individual components. The mathematical theory has been used to analyze two systems of biological significance: the coupling among chemical reactions and the stability properties of a 4-dimensional system describing the kinetics of a chemical transmitter.

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

Similar content being viewed by others

Literature

  • De Groot, S. R. 1963.Thermodynamics of Irreversible Processes. Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • De Sobrino, L. 1975. “The Glansdorff-Prigogine Thermodynamic Stability Criterion in the Light of Liapunov's Theory.”J. Theor. Biol.,54, 323–333.

    Article  Google Scholar 

  • Hahn, W. 1967.Stability of Motion. New York: Springer.

    Google Scholar 

  • Krasovskii, N. N. 1963.Stability of Motion. Stanford: Stanford University Press.

    Google Scholar 

  • Leibovic, K. N. L. 1975. “Analysis of Light Absorption and Response of Vertebrate Photoreceptor.”5th International Biophysics Congress. Copenhagen, Denmark.

  • — and F. Andrietti. 1977. “Analysis of a model for transmitter kinetics.”Biol. Cybernetics,27, 165–173.

    Article  MATH  Google Scholar 

  • Michel, A. N. 1974. “Stability Analysis of Interconnected Systems.”SIAM J. Control.,12 (3), 554–580.

    Article  MATH  MathSciNet  Google Scholar 

  • Rosen, R. 1968. “Some Comments on the Physico-Chemical Desciption of Biological Activity.”J. Theor. Biol.,18, 380–386.

    Article  Google Scholar 

  • Ŝiljak, D. D. 1972. “Stability of Large-Scale Systems.”Proc. Fifth World Congress of IFAC (Session 9, Nonlinear Systems): Paris.

  • — 1975. “When is a Complex Ecosystem Stable?.”Math. Biosci.,25, 25–50.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto di Fisiologia Generale e di Chimica, Biologica dell'Università degli Studi di Milano, Via Mangiagalli 32, 20133, Milano, Italy

    Francesco Andrietti

Authors
  1. Francesco Andrietti
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Andrietti, F. Interactions among biological systems: An analysis of asymptotic stability. Bltn Mathcal Biology 40, 839–851 (1978). https://doi.org/10.1007/BF02460610

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02460610

Keywords

Search

Navigation