Locating closed streamlines in 3D vector fields
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
Detection and Visualization of Closed Streamlines in Planar Flows
IEEE Transactions on Visualization and Computer Graphics
Finite approximations of Markov operators
Journal of Computational and Applied Mathematics
A non-equilibrium analysis and control framework for active queue management
Automatica (Journal of IFAC)
Invariant measures of tunable chaotic sources: robustness analysis and efficient estimation
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Computation of uncertainty distributions in complex dynamical systems
ACC'09 Proceedings of the 2009 conference on American Control Conference
Congestion and almost invariant sets in dynamical systems
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
Efficient optimal design of uncertain discrete time dynamical systems
Automatica (Journal of IFAC)
Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification
Advances in Data Analysis and Classification
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We present efficient techniques for the numerical approximation of complicated dynamical behavior. In particular, we develop numerical methods which allow us to approximate Sinai--Ruelle--Bowen (SRB)-measures as well as (almost) cyclic behavior of a dynamical system. The methods are based on an appropriate discretization of the Frobenius--Perron operator, and two essentially different mathematical concepts are used: our idea is to combine classical convergence results for finite dimensional approximations of compact operators with results from ergodic theory concerning the approximation of SRB-measures by invariant measures of stochastically perturbed systems. The efficiency of the methods is illustrated by several numerical examples.