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

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