Perturbative Expansion of the Fundamental Equation of Online User Dynamics for Describing Changes in Eigenfrequencies

The oscillation model has been proposed as a theoretical framework for describing user dynamics in online social networks. This model can represent 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.