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Author: Kurths, Jürgen × End date: 2022 × Start date: 2021 × End date: 2023 × Start date: 2020 × Subject: Systems ×

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    Statistical analysis of tipping pathways in agent-based models
    (Berlin ; Heidelberg : Springer, 2021) Helfmann, Luzie; Heitzig, Jobst; Koltai, Péter; Kurths, Jürgen; Schütte, Christof
    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.
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    Analysis of a bistable climate toy model with physics-based machine learning methods
    (Berlin ; Heidelberg : Springer, 2021) Gelbrecht, Maximilian; Lucarini, Valerio; Boers, Niklas; Kurths, Jürgen
    We propose a comprehensive framework able to address both the predictability of the first and of the second kind for high-dimensional chaotic models. For this purpose, we analyse the properties of a newly introduced multistable climate toy model constructed by coupling the Lorenz ’96 model with a zero-dimensional energy balance model. First, the attractors of the system are identified with Monte Carlo Basin Bifurcation Analysis. Additionally, we are able to detect the Melancholia state separating the two attractors. Then, Neural Ordinary Differential Equations are applied to predict the future state of the system in both of the identified attractors.