3 citations · 3 across the 5 of their papers we have counts for
5 papers
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…
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,…
Considering Slow Manifold Based Model Reduction for Multiscale Chemical Optimal Control Problems
Marcus Heitel, Robin Verschueren, Moritz Diehl +1
Finite-dimensional dissipative dynamical systems with multiple time-scales are obtained when modeling chemical reaction kinetics with ordinary differential equations. Such stiff sy…
An online slow manifold approach for efficient optimal control of multiple time-scale kinetics
Marcus Heitel, Dirk Lebiedz
Chemical reactions modeled by ordinary differential equations are finite-dimensional dissipative dynamical systems with multiple time-scales. They are numerically hard to tackle --…