The Combination of Topology and Nodes’ States Dynamics as an Early-warning Signal of Critical Transition in a Banking Network Model

摘要

Banking systems, modelled with networks, evolve over time overcoming critical points. Topology-oriented indicators of tipping points and early-warning signals of criticality in net- works do not reflect the gradual movement of a system towards a tipping point. Plenty of networks with SIR-like dynamics have restricted numbers of node states. In the case of banking networks, the range space of node states is continual, which allows an estimation of single bank remoteness from an insolvent state. Remoteness and velocity reflect change in the state per iteration and are considered in order to estimate the influence of node dynamics. Both node dynamics and topology are taken into account. We consider the positive and negative impact of interbank interactions (edge presence). Each edge is considered with weight and length parameters corresponding to the size of interbank lending and the number of iterations remaining before it expires. It was shown that the dropping well below zero of the presented indicator, is referred to as the potential of interactions, is a sign of a forthcoming tipping point. The introduced ? -Threatened set allows the detection of an approaching a tipping point in terms of nodes’ states.