Mixed mode oscillations in the Bonhoeffer-van der Pol oscillator with weak periodic perturbation
Mathematical Physics
2013-11-21 v1 math.MP
Abstract
Following the paper of K. Shimizu et al. (2011) we consider the Bonhoeffer-van der Pol oscillator with non-autonomous periodic perturbation. We show that the presence of mixed mode oscillations reported in that paper can be explained using the geometrical theory of singular perturbations. The considered model can be re-written as a 4-dimensional (locally 3-dimensional) autonomous system, which under certain conditions has a folded saddle-node singularity and additionally can be treated as a three time scale one.
Keywords
Cite
@article{arxiv.1311.5215,
title = {Mixed mode oscillations in the Bonhoeffer-van der Pol oscillator with weak periodic perturbation},
author = {E. Kutafina},
journal= {arXiv preprint arXiv:1311.5215},
year = {2013}
}