Complexity functions for networks: Dynamical hubs and complexity clusters

摘要

Highlights • A new characteristic, mean complexity is introduced for dynamical networks. • The characteristic determines “amounts of instability” of a dynamical network. • It allows to single out dynamical hubs and complexity clusters. Abstract A method for studying the behavior of the elements of dynamical networks is introduced. We measure the amount of instability stored at each element according to the value of the mean complexity related to this element. Elements with close values of the mean complexity can be unified into complexity clusters; elements with the smallest values of complexities form dynamical hubs. The effectiveness of the method is manifested by its successive application to networks of coupled Lorenz systems.