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 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.
Highlights
Understanding tipping pathways and tipping cascades in social systems are very important for our interconnected world
The aim of this paper is two-fold: (i) We propose a methodology how noise-induced tipping in high-dimensional agent-based models can be analysed by combining several existing methods such as nonlinear dimensionality reduction and Transition Path Theory [43,73]
In this paper we showed how to quantitatively study noise-induced tipping pathways in high-dimensional, stationary models of heterogeneous agents
Summary
Understanding tipping pathways and tipping cascades in social systems are very important for our interconnected world. Bifurcation diagrams of high-dimensional ABMs have already been studied [60,66], as well as the various bifurcation-induced transition pathways in a coupled social-ecological model [41], but to our knowledge noiseinduced tipping in agent-based models has not been considered yet. The more agents in the population exhibit behaviour A, the more likely an agent can be convinced by her social peers to switch from the opinion “one should do A” to “one should not do A”, since it may seem that the issue addressed by behaviour A is already sufficiently dealt with This negative feedback loop induces oscillatory dynamics. Note that we follow the convention to use uppercase letters X for random variables and lowercase letters x for their possible realizations
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