The Poincare-Bendixson theorem for monotone cyclic feedback systems

AbstractWe 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.

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