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math.DS2022
Approximating normally attracting invariant manifolds using trajectory-based optimization
Jörn Dietrich, Dirk Lebiedz
The numerical simulation of realistic reactive flows is a major challenge due to the stiffness and high dimension of the corresponding kinetic differential equations. Manifold-base…
math.DS2019★ 3 cited
A Spectral View on Slow Invariant Manifolds in Complex-Time Dynamical Systems
Jörn Dietrich, Dirk Lebiedz
Many real-analytic flows, e.g. in chemical kinetics, share a multiple time scale spectral structure. The trajectories of the corresponding dynamical systems are observed to bundle…
math.DS2019
Analytic continuation and differential geometry views on slow manifolds and separatrices
Dirk Lebiedz, Jörn Dietrich, Marcus Heitel +1
We start from a mechano-chemical analogy considering the time evolution of a homogeneous chemical reaction modeled by a nonlinear dynamical system (ordinary differential equation,…