Inferring connectivity of interacting phase oscillators

Abstract

The question as to how network topology properties influence network dynamical behavior has been extensively investigated. Here we treat the inverse problem, i.e., how to infer network connection topology from the dynamic evolution, and suggest a control based topology identification method. This method includes two steps: (i) driving the network to a steady state and (ii) inferring all elements of the connectivity matrix by exploiting information obtained from the observed steady state response of each node. We adopt different strategies for model-dependent (i.e., each local phase dynamics and coupling functions are known) and model-free (i.e., each local phase dynamics and coupling functions are unknown) cases and give detailed conditions for both cases under which network topology can be identified correctly. The influence of noise on topology identification is discussed as well. All proposed approaches are motivated and illustrated with networks of phase oscillators. We argue that these topology identification methods can be extended to general dynamical networks and are not restricted to only networks of phase oscillators.