Characterisation of local properties and prediction in chaotic dynamical systems

This work identifies regions in state space of conservative and dissipative chaotic systems that allow statements about future states or the predictability. This is done using two kinds of local exponents as well as ensemble studies. In conservative systems with trapping, the distribution of finite-time Lyapunov exponents (FTLE) has multiple maxima. These can be attributed to pieces of the trajectory that stay in the vicinity of islands of different orders. It is shown that in the vicinity of homoclinic tangencies regions of enhanced predictability exist, as measured by FTLE. Growth of finite errors is calculated using ensembles. For small errors it is the same as that calculated with maximum-growth exponents. The worst-case error grows exponentially for small, according to a power law for large prediction times. The influence of ensemble size on the accuracy of results is largest for the worst case, its error growth is the easiest to determine with a small ensemble.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Oldenburg

Year

2007

Author dc:creator

• Harle, Markus

• [Keine Schlagwörter von Autor/in vergeben.]

Repository record source_url

http://oops.uni-oldenburg.de/733

OAI identifier oai:identifier

oai:oops.uni-oldenburg.de:733