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Dynamics of noninvertibility in delay equations

Pages: 768 - 777, Issue Special, August 2005

 Abstract        Full Text (265.8K)              

Evelyn Sander - Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, United States (email)
E. Barreto - Dept. of Physics & Astronomy, George Mason University, Fairfax, VA 22030, United States (email)
S.J. Schiff - Dept of Psychology, The Krasnow Institute for Advanced Study and The Program in Neuroscience, George Mason University, Fairfax, VA 22030, United States (email)
P. So - Dept. of Physics & Astronomy, The Krasnow Institute for Advanced Study and The Program in Neuroscience, George Mason University, Fairfax, VA 22030, United States (email)

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 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.

Keywords:  Delay differential equations, noninvertibility, nonuniqueness.
Mathematics Subject Classification:  Primary:34K, Secondary:39B.

Received: September 2004;      Revised: April 2005;      Published: September 2005.