30 citations · 127 across the 20 of their papers we have counts for
20 papers
Collective variables for homophily-driven network rewiring dynamics
Sören Nagel, Stefanie Winkelmann, Péter Koltai +2
Stochastic network rewiring processes, in which edges dynamically rewire based on fixed node attributes, are widely used in applications ranging from social dynamics to neuroscienc…
Opinion Dynamics over Migration Networks
Lőrinc Márton, Stefanie Winkelmann, Mauricio J. del Razo +1
Opinions play a crucial role in shaping collective phenomena such as political polarization, cultural integration and demographic change. By continuously changing social environmen…
Energetic characterisation of transient clustering dynamics in aggregation-diffusion systems
Nathalie Wehlitz, Richard Scherzer, Carsten Hartmann +1
We investigate transient clustering dynamics in nonlocal aggregation-diffusion systems from an energetic perspective. Starting from a stochastic interacting particle system, we stu…
Data-driven Reduction of Transfer Operators for Particle Clustering Dynamics
Nathalie Wehlitz, Grigorios A. Pavliotis, Christof Schütte +1
We develop an operator-based framework to coarse-grain interacting particle systems that exhibit clustering dynamics. Starting from the particle-based transfer operator, we first c…
Accurate mean-field equation for voter model dynamics on scale-free networks
Marvin Lücke, Stefanie Winkelmann, Péter Koltai
Understanding the emergent macroscopic behavior of dynamical systems on networks is a crucial but challenging task. One of the simplest and most effective methods to construct a re…
Unfolding the geometric structure and multiple timescales of the urea-urease pH oscillator
Arthur V. Straube, Guillermo Olicón Méndez, Stefanie Winkelmann +2
We study a two-variable dynamical system modeling pH oscillations in the urea-urease reaction within giant lipid vesicles -- a problem that intrinsically contains multiple, well-se…
Approximating particle-based clustering dynamics by stochastic PDEs
Nathalie Wehlitz, Mohsen Sadeghi, Alberto Montefusco +3
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membr…
Multi-grid reaction-diffusion master equation: applications to morphogen gradient modelling
Radek Erban, Stefanie Winkelmann
The multi-grid reaction-diffusion master equation (mgRDME) provides a generalization of stochastic compartment-based reaction-diffusion modelling described by the standard reaction…
Partial mean-field model for neurotransmission dynamics
Alberto Montefusco, Luzie Helfmann, Toluwani Okunola +2
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microsc…
Learning Interpretable Collective Variables for Spreading Processes on Networks
Marvin Lücke, Stefanie Winkelmann, Jobst Heitzig +2
Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes…
Rate-limiting recovery processes in neurotransmission under sustained stimulation
Ariane Ernst, Nathalie Unger, Christof Schütte +2
At chemical synapses, an arriving electric signal induces the fusion of vesicles with the presynaptic membrane, thereby releasing neurotransmitters into the synaptic cleft. After a…
Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles
Arthur V. Straube, Stefanie Winkelmann, Felix Höfling
This theoretical study concerns a pH oscillator based on the urea-urease reaction confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hy…
Chemical diffusion master equation: formulations of reaction--diffusion processes on the molecular level
Mauricio J. del Razo, Stefanie Winkelmann, Rupert Klein +1
The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction--diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112:49,…
Large population limits of Markov processes on random networks
Marvin Lücke, Jobst Heitzig, Péter Koltai +2
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dim…
Synchronization and random attractors for reaction jump processes
Maximilian Engel, Guillermo Olicón-Méndez, Nathalie Unger +1
This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. A corresponding random d…
Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading
Stefanie Winkelmann, Johannes Zonker, Christof Schütte +1
Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost…
A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures
Alberto Montefusco, Christof Schütte, Stefanie Winkelmann
The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatiall…
Stochastic pH oscillations in a model of the urea-urease reaction confined to lipid vesicles
Arthur V. Straube, Stefanie Winkelmann, Christof Schütte +1
The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We study the confinement of the rea…
A probabilistic framework for particle-based reaction-diffusion dynamics using classical Fock space representations
Mauricio J. del Razo, Daniela Frömberg, Arthur V. Straube +3
The modeling and simulation of stochastic reaction-diffusion processes is a topic of steady interest that is approached with a wide range of methods. \rev{At the level of particle-…
From interacting agents to density-based modeling with stochastic PDEs
Luzie Helfmann, Natasa Djurdjevac Conrad, Ana Djurdjevac +2
Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the syst…