“Novel insights into the precursor theory of adaptive networks”

Leonhard Horstmeyer from the Complexity Science Hub Vienna at the Workshop: Predicting Transitions in Complex Systems at the Max Planck Institute for the Physics of Complex Systems

Abstract

The adaptive SIS model is one of the most elementary models in which the dynamics on the network is coupled to the dynamics of the network. We investigate the critical behavior of the network topology by looking at the densities of motives, the clustering, the compactness, the degree distribution and assortativity, the effective branching ratio and spectral distribution. The proximity to the persistence threshold can be sensed in some of these quantities long before the transition via the appearance of local maxima due to a crossover phenomenon. This is also reconcilable with the pair approximation. A good signal-to-noise ratio makes them novel candidates for precursors of the transition. We explain the mechanism that gives rise to this behavior and some caveats. We also discuss the issues that arise when fitting power laws to these quantities.