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The oscillation model has been proposed as a theoretical framework fordescribing user dynamics in online social networks. This model can model theuser dynamics generated by a particular network structure and allow its causalrelationships to be explicitly described. In this paper, by applyingperturbation theory to the fundamental equation of the oscillation model, weconfirm that we can explicitly trace, at least in principle, the changes inuser dynamics associated with changes in the network structure. Specifically,we formulate perturbative expansions up to infinite order, by drawing oninferences from regularities found in perturbative expansions; the accuracy ofperturbative expansions of finite order is evaluated by numerical experiments.

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