Vibrational resonance: a study with high-order word-series averaging
Abstract
We study a model problem describing vibrational resonance by means of a high-order averaging technique based on so-called word series. With the tech- nique applied here, the tasks of constructing the averaged system and the associ- ated change of variables are divided into two parts. It is first necessary to build recursively a set of so-called word basis functions and, after that, all the required manipulations involve only scalar coefficients that are computed by means of sim- ple recursions. As distinct from the situation with other approaches, with word- series, high-order averaged systems may be derived without having to compute the associated change of variables. In the system considered here, the construction of high-order averaged systems makes it possible to obtain very precise approxima- tions to the true dynamics.
Cite
@article{arxiv.1604.01215,
title = {Vibrational resonance: a study with high-order word-series averaging},
author = {Ander Murua and J. M. Sanz-Serna},
journal= {arXiv preprint arXiv:1604.01215},
year = {2016}
}