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We study a model problem describing vibrational resonance by means of ahigh-order averaging technique based on so-called word series. With the tech-nique applied here, the tasks of constructing the averaged system and theassoci- ated change of variables are divided into two parts. It is firstnecessary to build recursively a set of so-called word basis functions and,after that, all the required manipulations involve only scalar coefficientsthat are computed by means of sim- ple recursions. As distinct from thesituation with other approaches, with word- series, high-order averaged systemsmay be derived without having to compute the associated change of variables. Inthe system considered here, the construction of high-order averaged systemsmakes it possible to obtain very precise approxima- tions to the true dynamics.

Vibrational resonance: a study with high-order word-series averaging