Validity of numerical trajectories in the synchronization transition of complex systems

We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown {\it via} unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same non-hyperbolic properties.Comment: 4 pages, 4 figure

Schulpsychologische Beratung am Beispiel Gewalt in der Schule

Wild E, Pikowsky B. Schulpsychologische Beratung am Beispiel Gewalt in der Schule. In: Hofer M, Wild E, Pikowsky B, eds. Grundlagen pädagogisch-psychologischer Beratung. Bern: Huber; 1996: 115-144

Schulpsychologische Beratung

Pikowsky B, Wild E. Schulpsychologische Beratung. In: Hofer M, Wild E, Pikowsky B, eds. Grundlagen pädagogisch-psychologischer Beratung. Bern: Huber; 1996: 87-114

Application of transfer entropy to causality detection and synchronization experiments in tokamaks

Determination of causal-effect relationships can be a difficult task even in the analysis of time series. This is particularly true in the case of complex, nonlinear systems affected by significant levels of noise. Causality can be modelled as a flow of information between systems, allowing to better predict the behaviour of a phenomenon on the basis of the knowledge of the one causing it. Therefore, information theoretic tools, such as the transfer entropy, have been used in various disciplines to quantify the causal relationship between events. In this paper, Transfer Entropy is applied to determining the information relationship between various phenomena in Tokamaks. The proposed approach provides unique insight about information causality in difficult situations, such as the link between sawteeth and ELMs and ELM pacing experiments. The application to the determination of disruption causes, and therefore to the classification of disruption types, looks also very promising. The obtained results indicate that the proposed method can provide a quantitative and statistically sound criterion to address the causal-effect relationships in various difficult and ambiguous situations if the data is of sufficient quality