Section: New Results

Multiplicity and Stable Varieties of Time-delay Systems: A Missing Link

Multiple spectral values in dynamical systems are often at the origin of complex behaviors as well as unstable solutions. In this work, an unexpected property of multiple spectral values is emphasized. It has been shown that the variety corresponding to such a multiple root defines a stable variety for the steady state. Under mild assumptions, for the reduced examples we show that such a multiple spectral value is nothing else than the spectral abscissa.