Stochastic Approaches to Complexity (425. WE-Heraeus-Seminar)

Grunddaten zu diesem Projekt

Beschreibung

Measured data of complex animate and inanimate systems, ranging from turbulence to traffic flows or brain signals, are often represented by fluctuating time series. This signals have to be analyzed and interpreted in an appropriate way. In the case of nonlinear systems conventional methods like evaluating correlation functions or correlation matrices are not sufficient. The methods developed for nonlinear time series analysis like the estimation of Ljapunov exponents or fractal dimensions and the reconstruction of deterministic evolution equations rely on the assumption that dynamical fluctuations play a minor role. Complex systems typically consist of many subsystems acting on very short time scales. In contrast emergent features and cooperative phenomena evolve on a much slower time scale. The microscopic dynamics of the single subsystems can often be treated as fluctuations that interact dynamically with the collective variables that are responsible for the self-organization. In this case the fluctuations can become so important that the deterministic methods of nonlinear time series analysis fail. The goal of the seminar is to give an overview over the recent developements in the field of analyzing complex systems by stochastic methods. Talks from different scientific disciplines ranging from physics to medicineshall give the opportunity to identify challenges and to present possible solutions