Perturbative expansion of the fundamental equation of online user dynamics for describing changes in eigenfrequencies

TL;DR

This paper applies perturbation theory to the fundamental oscillation model of online user dynamics, enabling explicit tracing of how network structure changes influence user behavior, with validated finite-order approximations.

Contribution

It introduces a perturbative expansion method for the fundamental oscillation equation, allowing detailed analysis of network structure impacts on user dynamics.

Findings

Perturbative expansions can be formulated up to infinite order.

Finite-order expansions provide accurate approximations.

Numerical experiments confirm the method's effectiveness.

Abstract

The oscillation model has been proposed as a theoretical framework for describing user dynamics in online social networks. This model can model the user dynamics generated by a particular network structure and allow its causal relationships to be explicitly described. In this paper, by applying perturbation theory to the fundamental equation of the oscillation model, we confirm that we can explicitly trace, at least in principle, the changes in user dynamics associated with changes in the network structure. Specifically, we formulate perturbative expansions up to infinite order, by drawing on inferences from regularities found in perturbative expansions; the accuracy of perturbative expansions of finite order is evaluated by numerical experiments.