Agent-based modeling: Population limits, metastability and large deviations

Please always quote using this URN: urn:nbn:de:0297-zib-77309
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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, a continuous-time stochastic agent-based model is formulated, the corresponding Markov jump process is defined and its approximation by ordinary and stochastic differential equations (ODEs and SDEs, respectively) is described. We provide a functional and transparent framework which allows for rigorous analysis, avoids problems of ambiguity and delivers straightforward connections to other modeling approaches. We demonstrate the advantages of an SDE model for different scenarios of interacting agent systems with medium or large population sizes. In comparison to the ODE limit model, the SDE gives a higher order approximation of the underlying Markov jump process, both on a pathwise level and regarding the process' moments. In particular, the SDE approach is able to retain metastabilty in the dynamics, which is lost in a deterministic ODE description, and to capture the distribution of rare and unlikely extreme events. Here, we apply the theory of large deviations to show consistency of the distributions' remote tails.

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Author:Stefanie WinkelmannORCiD, Jan-Hendrik NiemannORCiD, Sarah WolfORCiD, Christof Schütte
Document Type:Article
Parent Title (German):Chaos: An Interdisciplinary Journal of Nonlinear Science
Year of first publication:2020