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
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
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:   <>  |
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Adi Ditkowski   <>