Journal of Dynamics and Differential Equations

, Volume 2, Issue 4, pp 367–421

The Poincare-Bendixson theorem for monotone cyclic feedback systems

  • John Mallet-Paret
  • Hal L. Smith
Article

DOI: 10.1007/BF01054041

Cite this article as:
Mallet-Paret, J. & Smith, H.L. J Dyn Diff Equat (1990) 2: 367. doi:10.1007/BF01054041

Abstract

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 systemcyclic systemmonotonicitynegative feedbackPoincare-Bendixson theorem

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