DYNAMICAL SYSTEMS Supplement Volume 2005 pp. 768{777 DYNAMICS OF NONINVERTIBILITY IN DELAY EQUATIONS

Abstract. 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 dierences between the dynamical properties of a delay equation and the familiar case of an ordinary dierential equation. We give speci c conditions for the existence of noninvertible solutions in delay equations, and describe the consequences of noninvertibility. 1. Introduction. Dela