Systems of Differential Delay Equations: Floquet Multipliers and Discrete Lyapunov Functions

Authors: Mallet-Paret J.¹; Sell G.R.²

Source: Journal of Differential Equations, Volume 125, Number 2, March 1996 , pp. 385-440(56)

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Abstract:

We define a discrete (integer-valued) Lyapunov function V for cyclic nearest neighbor systems of differential delay equations possessing a feedback condition. This extends analogous definitions for cyclic systems of ODE's, and for scalar differential delay equations. We relate the values of V to the real parts of the Floquet multipliers for such linear periodic systems, and thereby prove all Floquet subspaces are at most two-dimensional.

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