Journal
COMPUTATIONAL & APPLIED MATHEMATICS
Volume 34, Issue 1, Pages 81-92Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s40314-013-0105-8
Keywords
Folded saddle-node; Three time scale system; Mixed mode oscillation; Singular perturbation; Canard
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Funding
- Research Foundation Flanders (FWO) [G.0939.10N]
- Polish Ministry of Science and Higher Education
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Following the paper of Shimizu et al. (Phys Lett A 375:1566, 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 geometric singular perturbation theory. The considered model can be re-written as a four-dimensional (locally three-dimensional) autonomous system, which under certain conditions has a folded saddle-node singularity and additionally can be treated as a three time scale one.
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