Network susceptibilities: theory and applications

TL;DR

This paper introduces the concept of network susceptibilities to quantify how small parameter changes affect the collective dynamics of various networked systems, with applications to oscillator, power grid, and flow models.

Contribution

It defines vertex and edge susceptibilities, derives explicit formulas for oscillator networks near steady states, and demonstrates broad applicability to different network types.

Findings

Explicit formulas for network susceptibilities in oscillator models.

Applications to power grid and flow networks.

Susceptibilities depend on network topology and can be generalized.

Abstract

We introduce the concept of network susceptibilities quantifying the response of the collective dy- namics of a network to small parameter changes. We distinguish two types of susceptibilities: vertex susceptibilities and edge susceptibilities, measuring the responses due to changes in the properties of units and their interactions, respectively. We derive explicit forms of network susceptibilities for oscillator networks close to steady states and offer example applications for Kuramoto-type phase- oscillator models, power grid models and generic flow models. Focusing on the role of the network topology implies that these ideas can be easily generalized to other types of networks, in particular those characterizing flow, transport, or spreading phenomena. The concept of network susceptibil- ities is broadly applicable and may straightforwardly be transferred to all settings where networks responses of the collective dynamics to topological changes are essential.