Journal of Dynamics and Differential Equations

, Volume 2, Issue 4, pp 367–421 | Cite as

The Poincare-Bendixson theorem for monotone cyclic feedback systems

  • John Mallet-Paret
  • Hal L. Smith


We prove the Poincare-Bendixson theorem for monotone cyclic feedback systems; that is, systems inRn of the form
$$x_i = f_i (x_i , x_{i - 1} ), i = 1, 2, ..., n (\bmod n).$$
We apply our results to a variety of models of biological systems.

Key words

Cellular control system cyclic system monotonicity negative feedback Poincare-Bendixson theorem 


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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • John Mallet-Paret
    • 1
  • Hal L. Smith
    • 2
  1. 1.Division of Applied MathematicsBrown UniversityProvidence
  2. 2.Department of MathematicsArizona State UniversityTempe

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