Statistical Analysis of Tipping Pathways in Agent-Based Models

Abstract

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 can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here, we are concerned with studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to the 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.

References in corpus (22)

• Community structure in social and biological networks
• Synchronization in complex networks
• Networks beyond pairwise interactions: structure and dynamics
• Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system
• Opinion dynamics: models, extensions and external effects
• Rescuing ecosystems from extinction cascades through compensatory perturbations
• Galerkin Approximation of Dynamical Quantities using Trajectory Data
• Computing Committor Functions for the Study of Rare Events Using Deep Learning
• A network-based microfoundation of Granovetter's threshold model for social tipping
• Three faces of node importance in network epidemiology: Exact results for small graphs
• Sparse eigenbasis approximation: multiple feature extraction across spatiotemporal scales with application to coherent set identification
• Flows in Complex Networks: Theory, Algorithms, and Application to Lennard-Jones Cluster Rearrangement
• Transition paths of marine debris and the stability of the garbage patches
• Learning forecasts of rare stratospheric transitions from short simulations
• Extending Transition Path Theory: Periodically-Driven and Finite-Time Dynamics
• Stochastic basins of attraction and generalized committor functions
• Path properties of atmospheric transitions: illustration with a low-order sudden stratospheric warming model
• Epidemic extinction in networks: Insights from the 12,110 smallest graphs
• Equation-Free Multiscale Computations in Social Networks: from Agent-based Modelling to Coarse-grained Stability and Bifurcation Analysis
• A semigroup method for high dimensional committor functions based on neural network
• Cycle flow based module detection in directed recurrence networks
• Learning emergent PDEs in a learned emergent space

Cited by in corpus (4)

• Learning forecasts of rare stratospheric transitions from short simulations
• Transition paths of North Atlantic Deep Water
• Data-driven transition path analysis yields a statistical understanding of sudden stratospheric warming events in an idealized model
• Large population limits of Markov processes on random networks