The proposed research cooperation focuses on the modeling and control of complex networks and systems. From a microscopic point of view, complex systems are characterized by the dynamics of single parts such as production goods or individuals in crowds. Naturally, the dynamics is driven by a deterministic part but can also be affected by stochastic events such as machine failures or random decisions. The classical approach is the derivation of exact macroscopic equations for conserved quantities on large time scales, where the total information of the transient regimes is reduced. We will derive approximate macroscopic models, which are able to handle transient regimes also including stochastic effects. Further, we extend these ideas to network models by introducing meaningful coupling conditions and to formulate optimal control problems. Exemplarily we focus on high volume or large production systems as well as pedestrian dynamics.
The common interest among both teams (University of Mannheim, Germany and Arizona State University, USA) is the development of mathematical tools and methods for the modeling and dynamics of complex flows in networks on all time scales. The goal is to exchange ideas, recent results and techniques to new applications and in different contexts. Major steps in pursuing these studies include an extensive discussion of cross-sectional approaches like hierarchical modeling, mean-field theory and multi-scale simulation.
Key words: stochastic complex systems, hierarchical modeling, analysis and numerical simulation
Funding: DAAD within the project „PPP USA 2019/2020“; travel expenses for two years
Duration: 01/2019 - 12/2020