Dynamics of noninvertibility in delay equations

Evelyn Sander; E. Barreto; S.J. Schiff; P. So

doi:10.3934/proc.2005.2005.768

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2005, Volume 2005: 768-777. Doi: 10.3934/proc.2005.2005.768 open access

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Dynamics of noninvertibility in delay equations

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

Received: September 2004

Revised: April 2005

Published: August 2005

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

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

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