Statistical analysis of tipping pathways in agent-based models
Institute of Mathematics, Freie Universität Berlin, Berlin, Germany
2 Zuse Institute Berlin, Berlin, Germany
3 Department of Complexity Science, Potsdam Institute for Climate Impact Research, Potsdam, Germany
4 Department of Physics, Humboldt University, Berlin, Germany
Accepted: 31 May 2021
Published online: 18 June 2021
Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach.
© The Author(s) 2021
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