Regensburg 2013 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 12: Nonlinear Dynamics, Synchronization and Chaos I

DY 12.11: Talk

Tuesday, March 12, 2013, 12:15–12:30, H48

Statistics, Predictability and Dynamics of Critical Transitions — •Xiaozhu Zhang¹, Christian Kühn², and Sarah Hallerberg¹ — ¹Network Dynamics Group, Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany — ²Vienna University of Technology, Institute for Analysis and Scientific Computing, 1040 Vienna, Austria

Critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socio-economic changes and climate transitions between ice-ages and warm-ages. From Bifurcation theory we can expect a critical transition to be announced by a decreased recovery from external perturbations. The consequences of this critical slowing down have been observed as an increase in variance and correlation before to the transition happens. However, it is not clear, whether these changes in observation variables are statistically relevant such that they could be used as predictors for critical transitions. In this contribution we investigate the predictability of critical transitions in the Van der Pol Oscillator under the influence of external noise. We focus especially on the statical analysis of the success of predictions and the overall predictability of the system.