Tel Aviv University School of Mathematical Sciences Applied Mathematics Seminar Date: Tuesday January 11th, 2011, 15:10 Place: Schreiber Bldg, Room 309 Speaker: Gadi Fibich Tel Aviv University Title: Aggregate Diffusion Dynamics in Agent-Based Models with a Spatial Structure Abstract: The diffusion or adoption of new products (such as fax machines, skype, facebook, Ipad, etc.) is one of the key problems in Marketing research. In recent years, this problem was often studied numerically, using agent-based models (ABMs). In this talk I will focus on analysis of the aggregate diffusion dynamics in ABMs with a spatial structure. In one-dimensional ABMs, the aggregate diffusion dynamics can be explicitly calculated, without using the mean-field approximation. In multidimensional ABMs, we introduce a clusters-dynamics approach, and use it to derive an analytic approximation of the aggregate diffusion dynamics. The clusters-dynamics approximation shows that the aggregate diffusion dynamics does not depend on the average distance between individuals, but rather on the expansion rate of clusters of adopters. Therefore, the grid dimension has a large effect on the aggregate adoption dynamics, but a small-world structure and heterogeneity among individuals have only a minor effect. Our results suggest that the one-dimensional model and the fully-connected Bass model provide a lower bound and an upper bound, respectively, for the aggregate diffusion dynamics in agent-based models with "any" spatial structure. This is joint work with Ro'i Gibori and Eitan Muller For information about future seminars, see <http://www.tau.ac.il/~adid/AM_seminar_2010-2011/AM_seminar_2010-2011.html> ______________________________________________________________________ Dr. Adi Ditkowski | Department of Applied Mathematics | School of Mathematical Sciences phone: 972-3-640-5987 | Tel Aviv University, fax : 972-3-640-9357 | Tel Aviv, 69978 Israel email: <adid@post.tau.ac.il> | ______________________________________________________________________ --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Adi Ditkowski <adid@post.tau.ac.il>