**Stochastic Bifurcation Theory**

January 13-15, 2003

The workshop was the start of
a new interdisciplinary research project "Stochastic bifurcation
theory" at the University of Amsterdam, with a grant from the
"Centraal Onderzoeksfonds". This is a joint project involving groups
from the Mathematics Institute, from the Department of Psychology and the
Department of Econometrics.

The scientific background of the workshop can
be described as follows. Dynamical systems provide a natural framework to study
processes that depend on time. For example, the evolution of the weather, the
behavior of stock prices, macroeconomic fluctuations and various neural
processes can all be modeled using techniques from dynamical system theory.
Essentially two different approaches may be distinguished: deterministic and
stochastic.

It became clear in the past decade that
purely deterministic systems are not suitable to describe real life processes.
This is certainly true in models that originate from behavioral sciences and
economics where individual behavior plays a role. A combined
deterministic-stochastic framework possibly provides a more suitable framework
to embed real life problems. However, very little is known on bifurcation
theory in a stochastic environment.

This workshop aimed to bring together people
from various disciplines, mathematics, economic sciences and human sciences, to
discuss theory and problems of random dynamical systems and stochastic
bifurcation theory. Its goal can be summarized by the term learnshop. The talks
that were held, ranged from a description of applications from human sciences
and economic sciences, to discussions of mathematical aspects of random
dynamical systems, bifurcations, and time series analysis. On several occasions
they gave rise to animated discussions, so that the goal of being a learnshop
was achieved.

**A.J.** **Homburg**
(UvA, The Netherlands)

**R.** **de Vilder**
(UvA, The Netherlands)