28 citations · 73 across the 20 of their papers we have counts for
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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…
On Analytical and Topological Properties of Separatrices in 1-D Holomorphic Dynamical Systems and Complex-Time Newton Flows
Marcus Heitel, Dirk Lebiedz
Separatrices divide the phase space of some holomorphic dynamical systems into separate basins of attraction or 'stability regions' for distinct fixed points. 'Bundling' (high dens…
On Differential Geometric Formulations of Slow Invariant Manifold Computation: Geodesic Stretching and Flow Curvature
Johannes Poppe, Dirk Lebiedz
The theory of slow invariant manifolds (SIMs) is the foundation of various model-order reduction techniques for dissipative dynamical systems with multiple time-scales, e.g. in che…
Stretching-Based Diagnostics in a Differential Geometry Setting
Johannes Poppe, Dirk Lebiedz
The identification of slow invariant manifolds (SIMs) is an essential part in model-order reduction for reactive systems. The mathematical definition of the SIM by Fenichel can be…
Characterization of Separatrices in Holomorphic Dynamical Systems
Marcus Heitel, Dirk Lebiedz
Multiple time scales in dynamical systems lead to a bundling of trajectories onto slow invariant manifolds (SIMs). Although they are absent in two-dimensional holomorphic dynamical…
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,…