# American Institute of Mathematical Sciences

2005, 2005(Special): 768-777. doi: 10.3934/proc.2005.2005.768

## Dynamics of noninvertibility in delay equations

 1 Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, United States 2 Dept. of Physics & Astronomy, George Mason University, Fairfax, VA 22030, United States 3 Dept of Psychology, The Krasnow Institute for Advanced Study and The Program in Neuroscience, George Mason University, Fairfax, VA 22030, United States 4 Dept. of Physics & Astronomy, The Krasnow Institute for Advanced Study and The Program in Neuroscience, George Mason University, Fairfax, VA 22030, United States

Received  September 2004 Revised  April 2005 Published  September 2005

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 di erences between the dynamical properties of a delay equation and the familiar case of an ordinary di erential equation. We give speci c conditions for the existence of noninvertible solutions in delay equations, and describe the consequences of noninvertibility.
Citation: Evelyn Sander, E. Barreto, S.J. Schiff, P. So. Dynamics of noninvertibility in delay equations. Conference Publications, 2005, 2005 (Special) : 768-777. doi: 10.3934/proc.2005.2005.768
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