Delay Differential Equations and Applications

This book groups material that was used for the Marrakech 2002 School on Delay Di?erential Equations and Applications. The school was held from September 9-21 2002 at the Semlalia College of Sciences of the Cadi Ayyad University, Marrakech, Morocco. 47 participants and 15 instructors originating from 21 countries attended the school. Fin- cial limitations only allowed support for part of the people from Africa andAsiawhohadexpressedtheirinterestintheschoolandhadhopedto come. Theschoolwassupportedby?nancementsfromNATO-ASI(Nato advanced School), the International Centre of Pure and Applied Mat- matics (CIMPA, Nice, France) and Cadi Ayyad University. The activity of the school consisted in courses, plenary lectures (3) and communi- tions (9), from Monday through Friday, 8. 30 am to 6. 30 pm. Courses were divided into units of 45mn duration, taught by block of two units, with a short 5mn break between two units within a block, and a 25mn break between two blocks. The school was intended for mathematicians willing to acquire some familiarity with delay di?erential equations or enhance their knowledge on this subject. The aim was indeed to extend the basic set of knowledge, including ordinary di?erential equations and semilinearevolutionequations,suchasforexamplethedi?usion-reaction equations arising in morphogenesis or the Belouzov-Zhabotinsky ch- ical reaction, and the classic approach for the resolution of these eq- tions by perturbation, to equations having in addition terms involving past values of the solution.

Inhalt
HISTORY OF DELAY EQUATIONS.- HISTORY OF DELAY EQUATIONS.- GENERAL RESULTS AND LINEAR THEORY OF DELAY EQUATIONS IN FINITE DIMENSIONAL SPACES.- SOME GENERAL RESULTS AND REMARKS ON DELAY DIFFERENTIAL EQUATIONS.- LINEAR AUTONOMOUS FUNCTIONAL DIFFERENTIAL EQUATIONS.- HOPF BIFURCATION, CENTRE MANIFOLDS AND NORMAL FORMS FOR DELAY DIFFERENTIAL EQUATIONS.- VARIATION OF CONSTANT FORMULA FOR DELAY DIFFERENTIAL EQUATIONS.- TO HOPF BIFURCATION THEORY FOR DELAY DIFFERENTIAL EQUATIONS.- AN ALGORITHMIC SCHEME FOR APPROXIMATING CENTER MANIFOLDS AND NORMAL FORMS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS.- NORMAL FORMS AND BIFURCATIONS FOR DELAY DIFFERENTIAL EQUATIONS.- FUNCTIONAL DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONAL SPACES.- A THEORY OF LINEAR DELAY DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONAL SPACES.- THE BASIC THEORY OF ABSTRACT SEMILINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONDENSE DOMAIN.- MORE ON DELAY DIFFERENTIAL EQUATIONS AND APPLICATIONS.- DYNAMICS OF DELAY DIFFERENTIAL EQUATIONS.- DELAY DIFFERENTIAL EQUATIONS IN SINGLE SPECIES DYNAMICS.- WELL-POSEDNESS, REGULARITY AND ASYMPTOTIC BEHAVIOUR OF RETARDED DIFFERENTIAL EQUATIONS BY EXTRAPOLATION THEORY.- TIME DELAYS IN EPIDEMIC MODELS.