Dynamics of Noninvertibility in Delay Equations

Models with a time delay often occur, since there is a naturally occurring delay in the transmission of information. A model with a delay can be noninvertible, which in turn leads to qualitative differences between the dynamical properties of a delay equation and the familiar case of an ordinary differential equation. We give specific conditions for the existence of noninvertible solutions in delay equations, and describe the consequences of noninvertibility.