TY - JOUR A1 - Helfmann, Luzie A1 - Heitzig, Jobst A1 - Koltai, Péter A1 - Kurths, Jürgen A1 - Schütte, Christof T1 - Statistical analysis of tipping pathways in agent-based models JF - Eur. Phys. J. Spec. Top. N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1140/epjs/s11734-021-00191-0 VL - 230 SP - 3249 EP - 3271 ER - TY - JOUR A1 - Lücke, Marvin A1 - Heitzig, Jobst A1 - Koltai, Péter A1 - Molkethin, Nora A1 - Winkelmann, Stefanie T1 - Large population limits of Markov processes on random networks JF - Stochastic Processes and their Applications N2 - We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each discrete state in the system, or in certain subsystems, and general conditions for the convergence of the collective variable dynamics to a mean-field ordinary differential equation are proved. We discuss the convergence to this mean-field limit for a continuous-time noisy version of the so-called "voter model" on Erdős-Rényi random graphs, on the stochastic block model, as well as on random regular graphs. Moreover, a heterogeneous population of agents is studied. For each of these types of interaction networks, we specify the convergence conditions in dependency on the corresponding model parameters. Y1 - 2023 U6 - https://doi.org/10.1016/j.spa.2023.09.007 VL - 166 ER - TY - JOUR A1 - Lücke, Marvin A1 - Winkelmann, Stefanie A1 - Koltai, Peter T1 - Accurate mean-field equation for voter model dynamics on scale-free networks JF - Physical Review E N2 - Understanding the emergent macroscopic behavior of dynamical systems on networks is a crucial but challenging task. One of the simplest and most effective methods to construct a reduced macroscopic model is given by mean-field theory. The resulting approximations perform well on dense and homogeneous networks but poorly on scale-free networks, which, however, are more realistic in many applications. In this paper, we introduce a modified version of the mean-field approximation for voter model dynamics on scale-free networks. The two main deviations from classical theory are that we use degree-weighted shares as coarse variables and that we introduce a correlation factor that can be interpreted as slowing down dynamics induced by interactions. We observe that the correlation factor is only a property of the network and not of the state or of parameters of the process. This approach achieves a significantly smaller approximation error than standard methods without increasing dimensionality. Y1 - 2026 U6 - https://doi.org/10.1103/vkpx-5cvt VL - 113 ER -