The Poincare-Bendixson theorem for monotone cyclic feedback systems with delay

We consider cyclic nearest neighbor systems of differential delay equations, in which the coupling between neighbors possesses a monotonicity property. Using a discrete (integer-valued) Lyapunov function, we prove that the Poincare-Bendixson theorem holds for such systems. We also obtain results on piecewise monotonicity and stability of periodic solutions of such systems. (C) 1996 Academic Press, Inc.