Bulletin of Mathematical Biology

, Volume 40, Issue 6, pp 839–851 | Cite as

Interactions among biological systems: An analysis of asymptotic stability

  • Francesco Andrietti
Article

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.

Keywords

Asymptotic Stability Composite System Negative Real Part Dynamical System Theory Boundedness Property 

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Copyright information

© Society for Mathematical Biology 1978

Authors and Affiliations

  • Francesco Andrietti
    • 1
  1. 1.Istituto di Fisiologia Generale e di ChimicaBiologica dell'Università degli Studi di MilanoMilanoItaly

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