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)