By: David Kleinhans
From: Univ. Gothenburg, Sweden
At: Complexo Interdisciplinar, Anfiteatro
Complex systems involve a huge amount of degrees of freedoms often interacting in a nonlinear manner. The efforts needed e.g. for the numerical simulation of turbulent flows show, that the characterisation of the dynamics of such systems in general is very complicated even if the interactions between the microscopic degrees of freedom are known to a great extent. In many systems of practical relevance such details, however, are not available. What can we then do on these systems?
A way out has been motivated by H. Haken some decades ago. Haken demonstrated, that stochastic differential equations can exhibit an adequate and rather precised description of complex systems as long as the dynamics of macroscopic order parameters are concerned. I will present and discuss methods for the estimation of stochastic dynamics from measured data on complex systems for the case that details of the internal dynamics are not available. The procedure is exemplified on date from turbulent flows, medical applications, traffic flows and biological applications.