CSH RESEARCHER TUAN MINH PHAM WILL PRESENT HIS WORK (RESEARCH TOGETHER WITH LEONARD HORSTEMYER; JAN KORBEL AND STEFAN THURNER) AT THE CONFERENCE TITLED “INTERACTING TIPPING ELEMENT IN THE NATURAL AND SOCIAL COMPONENTS OF THE EARTH SYSTEM” BY THE WILEHLM UND ELSE HERAEUS-STIFTUNG IN AUGUST 2021:
Predicting collapse in adaptive (dynamic) networked systems has received much less attention than finding precursors of collapse in static networks. In the most generic sense, collapse in co-evolutionary systems often may happen endogenously via a self-organisation of the network structure into a critical state where the states of nodes and links change irreversibly and drastically. Therefore, it seems hard or even impossible to answer the question of whether an adaptive networked system is about to collapse in the near future if the detailed structural information is unknown. In contrast to this intuition, based on classical results of algebraic graph theory, we introduce a new approach – so-called Eigenvector Quantisation which gives a positive answer to this question for linear (or linearized) dynamical systems.
The presented approach offers a novel early-warning signals which uses only the state variables’ (units) timeseries for the detection of a critical state of the underlying network of interactions between these units. It is shown that the critical state with a single directed cycle in the network can be detected by a “quantization effect” of node states, that exists as a direct consequence of a corollary of the Perron–Frobenius theorem. Within our framework, the likelihood of an impending collapse in the Jain-Krishna model of catalytic interactions can be estimated with high accuracy. We also show how the approach can be applied to other models of epidemic spreading and age-structured populations.