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

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.

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