Repository: Freie Universität Berlin, Math Department

Agent-based modeling: Population limits and large timescales

Niemann, Jan-Hendrik and Winkelmann, Stefanie and Wolf, S. and Schütte, Christof (2021) Agent-based modeling: Population limits and large timescales. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31 (3).

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Modeling, simulation, and analysis of interacting agent systems is a broad field of research, with existing approaches reaching from informal descriptions of interaction dynamics to more formal, mathematical models. In this paper, we study agent-based models (ABMs) given as continuous-time stochastic processes and their pathwise approximation by ordinary and stochastic differential equations (SDEs) for medium to large populations. By means of an appropriately adapted transfer operator approach, we study the behavior of the ABM process on long time scales. We show that, under certain conditions, the transfer operator approach allows us to bridge the gap between the pathwise results for large populations on finite timescales, i.e., the SDE limit model, and approaches built to study dynamical behavior on long time scales like large deviation theory. The latter provides a rigorous analysis of rare events including the associated asymptotic rates on timescales that scale exponentially with the population size. We demonstrate that it is possible to reveal metastable structures and timescales of rare events of the ABM process by finite-length trajectories of the SDE process for large enough populations. This approach has the potential to drastically reduce computational effort for the analysis of ABMs.

Item Type:Article
Subjects:Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2970
Deposited By: Monika Drueck
Deposited On:02 May 2023 10:42
Last Modified:02 Feb 2024 12:46

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