Summer School on Mathematics in Biology in Medicine

September 20-24, 2004

Rafael Bravo

Biography

Rafael Bravo is lecturer and researcher in the Department of Mathematics of the University of Alcal‡, a medium size university in the outskirts of Madrid.
His lectures address the subject of basic dynamical systems and models for Environmental Sciences students. His research work has mainly consisted in the development of so-called variables aggregation methods and its applications in studying population dynamics (see for instance (1-3)). In the mathematical treatment of biological problems, in particular in ecology, it is frequently needed to study models, dynamical systems, of high complexity which are often very difficult to handle analytically. The task of the analytical study of some of those systems is simplified by means of variables aggregation methods which consist in describing the asymptotical behaviour of the complex system with the help of a reduced system containing a few global variables. The main ingredient that allows this reduction is the existence of different time scales involved in the system. Rafael Bravo leads a research group who is involved in collaborative projects with groups in France, P. Auger (U. of Lyon 1) and J.C. Poggiale (U. of Marseille), and in Morocco, M.L. Hbid (U. of Marrakech). They have already organized two successful conferences in Alcalá, the 1st and 2nd Alcalá International Conference on Mathematical Ecology (http://euromedbiomath.aicme.free.fr). The second was held in September 5-9, 2003, and was attended by more than 250 participants, and included about 230 presentations. Some of these works are going to be published as special issues of five well reputed journals. Rafael Bravo is member of the board of the European Society for the Mathematical and Theoretical Biology, ESMTB, where he is mainly concerned with the organization of workshops and summer schools.

1. R. Bravo de la Parra, E. S‡nchez, O. Arino and P. Auger (1999) A Discrete Model with Density Dependent Fast Migration, Mathematical Biosciences 157, 91-109.
2. P. Auger and R. Bravo de la Parra (2000) Methods of aggregation of variables in population dynamics, C. R. Acad. Sci. Paris, Sciences de la vie 323, 665-674.
3. L. Sanz and R. Bravo de la Parra (2001) Time scales in a non autonomous linear discrete model, Mathematical Models and Methods in Applied Sciences 11, 1203-1235.