Jens Starke

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Don Ross

University College Cork

Daniel Weiskopf

Georgia State University

Fabio Cuzzolin

Oxford Brookes University

Roma Siugzdaite

Ghent University

Kashif Hayat

Quaid-i-Azam University, Islamabad, Pakistan

pragya rathore

Sanghvi Institute of Management & Science, Indore

MILTON DALL'AGLIO

Universidade Estadual Paulista "Júlio de Mesquita Filho"

Huinny Asaloei

University of Indonesia

Wilasinee Yoochatchaval

Kasetsart University

Asma Naim

University of Karachi

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Papers by Jens Starke

Detecting Stability and Bifurcation Points in Control-Based Continuation for a Physical Experiment of the Zeeman Catastrophe Machine

Siam Journal on Applied Dynamical Systems, Jun 23, 2023

Convergence of equation-free methods in the case of finite time scale separation with application to deterministic and stochastic systems (supplementary material)

A common approach to studying high-dimensional systems with emergent low-dimensional behavior is ... more A common approach to studying high-dimensional systems with emergent low-dimensional behavior is based on lift-evolve-restrict maps (called equation-free methods): first, a user-defined lifting operator maps a set of low-dimensional coordinates into the high-dimensional phase space, then the high-dimensional (microscopic) evolution is applied for some time, and finally a user-defined restriction operator maps down into a low-dimensional space again. We prove convergence of equation-free methods for finite time-scale separation with respect to a method parameter, the so-called healing time. More precisely, if the high-dimensional system has an attracting invariant manifold with smaller expansion and attraction rates in the tangential direction than in the transversal direction (normal hyperbolicity), and restriction and lifting satisfy some generic transversality conditions, then the implicit formulation of the lift-evolve-restrict procedure generates an approximate map that converges to the flow on the invariant manifold for healing time going to infinity. In contrast to all previous results, our result does not require the time scale separation to be large. A demonstration with Michaelis-Menten kinetics shows that the error estimates of our theorem are sharp. The ability to achieve convergence even for finite time scale separation is especially important for applications involving stochastic systems, where the evolution occurs at the level of distributions, governed by the Fokker-Planck equation. In these applications the spectral gap is typically finite. We investigate a low-dimensional stochastic differential equation where the ratio between the decay rates of fast and slow variables is 2.

Cost oriented competing processes — a new handling of assignment problems

Springer eBooks, 1996

The method of Cost Oriented Competing Processes (COCP) is a new approach to handle assignment pro... more The method of Cost Oriented Competing Processes (COCP) is a new approach to handle assignment problems and combinatorial optimization problems. The COCP method works with a system of nonlinear coupled ordinary differential equations with suitable stable points. In contrast to many other techniques, this method can easily be generalized and adapted to different assignment problems, even to those of higher order and with additional constraints. In assignment problems of higher order, the single costs which have to be considered for the total costs depend on several decisions instead of only one decision as in linear assignment problems. The handling of those higher order assignment problems is important for several scheduling problems such as manufacturing planning and time table planning. Keywords Combinatorial optimization, assignment problems, quadratic assignment problems (QAP), assignment problems of higher order, scheduling, selforganization, manufacturing planning, neural networks 1 LINEAR ASSIGNMENT PROBLEMS In an assignment problem (see e.g. (Eiselt et al., 1987), (Zimmermann, 1990)) there are decision variables Xij E {O, I}. The aim of linear assignment problems is to minimize Leij' Xij i,)

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