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The Poincare-Bendixson theorem for monotone cyclic feedback systems

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Abstract

We prove the Poincare-Bendixson theorem for monotone cyclic feedback systems; that is, systems inR n 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.

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Mallet-Paret, J., Smith, H.L. The Poincare-Bendixson theorem for monotone cyclic feedback systems. J Dyn Diff Equat 2, 367–421 (1990). https://doi.org/10.1007/BF01054041

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  • DOI: https://doi.org/10.1007/BF01054041

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