Applied Computational Mathematics Division


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Approximating Limit Cycles of an Autonomous Delay Differential Equation

David Gilsinn
Information Technology Laboratory, Mathematical and Computational Sciences Division

Tuesday, September 28, 2004 15:00-16:00,
NIST North (820), Room 145
Gaithersburg
Tuesday, September 28, 2004 13:00-14:00,
Room 4550
Boulder

Abstract: This talk discusses an unusual existence theorem for periodic solutions of an autonomous delay differential equation. The result is unusual in the sense that if by some means, e.g. Galerkin approximations, an approximate frequency and formal periodic solution is computed that satisfies a certain noncriticality condition, to be defined in the talk, then it is possible to prove the existence of an exact frequency and periodic solution in a neighborhood of the approximate frequency and periodic solution and provide a numerical bound on that neighborhood. Obtaining this numerical bound of course requires computing a number of parameters. A set of algorithms for computing these parameters will be given along with an application to a Van der Pol delay differential equation with unit delay.

Speaker Bio: David E. Gilsinn is a Senior Mathematician with the Mathematical and Computational Sciences Division of the National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland, USA. He received the BS degree in Mathematics at Georgetown University in 1964, the MS degree in Mathematics at Rutgers--The State University in 1966, and the PhD degree in Mathematics at Georgetown University in 1969. From 1969 to 1970 he was a Senior Mathematician with Melpar, Inc., designing aircraft pilot performance measures. From 1970 to 2000 he was a Senior Mathematician with the Technical Analysis Division (abandoned by NIST in 1974), the precursor to ITL, the Institute for Computer Science and Technology (ICST), and MEL and its precursor CME at NIST doing applied research in multidiscipline areas from, for example, developing network flow algorithms to predict commodity and vehicle flows through networks to developing the NBS test programs to evaluate compliance of commercial implementations of BASIC with the ANSI and FIPS standard for BASIC. During his career with MEL he has developed algorithms for optical scattering problems, performed finite element analysis for the design of major structural components of high precision coordinate measuring machines, and developed statistical and analytical methods to analyze machine tool errors. His awards include The Applied Research Award, National Institute of Standards and Technology, Dec. 8, 1994 (Group Award) and the Department of Commerce Bronze Medal, Dec. 8, 1994 (Group Award). He joined MCSD in 2000 and has become involved with BFRL in developing algorithms for object recognition at construction sites. His main areas of research span the fields of dynamical systems, optimization, and image processing. He is the author or co-author of more than 50 technical articles and reports and is a member of Sigma Xi, SIAM, and ASME.

Presentation Slides: PDF

Contact: P. M. Ketcham

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.