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

@inproceedings{MalletParet1996SystemsOD,
  title={Systems of Differential Delay Equations: Floquet Multipliers and Discrete Lyapunov Functions},
  author={John Mallet-Paret and George R. Sell},
  year={1996}
}
We de ne a discrete (integer-valued) Lyapunov function V for cyclic nearest neighbor systems of di erential delay equations possessing a feedback condition. This extends analogous de nitions for cyclic systems of ODE's, and for scalar di erential 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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