Statistical analysis of tipping pathways in agent-based models
- 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.
| Author: | Luzie HelfmannORCiD, Jobst Heitzig, Péter Koltai, Jürgen Kurths, Christof Schütte |
|---|---|
| Document Type: | Article |
| Parent Title (English): | Eur. Phys. J. Spec. Top. |
| Volume: | 230 |
| First Page: | 3249 |
| Last Page: | 3271 |
| Date of first Publication: | 2021/06/18 |
| ArXiv Id: | http://arxiv.org/abs/2103.02883 |
| DOI: | https://doi.org/10.1140/epjs/s11734-021-00191-0 |

