Dynamics of noninvertibility in delay equations

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

Dynamics of noninvertibility in delay equations

Evelyn Sander ^1, , E. Barreto ^2, , S.J. Schiff ^3, and P. So ^4,

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

Abstract
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Under a Creative Commons license

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 specic conditions for the existence of noninvertible solutions in delay equations, and describe the consequences of noninvertibility.

Keywords: Delay differential equations, noninvertibility, nonuniqueness..

Mathematics Subject Classification: Primary:34K, Secondary:39.

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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