The Poincare-Bendixson Theorem for Monotone Cyclic Feedback Systems with Delay

Authors: Mallet-Paret J.¹; Sell G.R.²

Source: Journal of Differential Equations, Volume 125, Number 2, March 1996 , pp. 441-489(49)

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Abstract:

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.

Language: English

Document Type: Research article

Affiliations: 1: Division of Applied Mathematics, Brown University, Providence, Rhode Island, 02912 2: School of Mathematics, University of Minnesota, Minneapolis, Minnesota, 55455

Publication date: 1996-03-01