Canard Explosion in Delay Differential Equations
Journal of Dynamics and Differential Equations, ISSN: 1572-9222, Vol: 28, Issue: 2, Page: 471-491
2016
- 8Citations
- 5Captures
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Article Description
We analyze canard explosions in delay differential equations with a one-dimensional slow manifold. This study is applied to explore the dynamics of the van der Pol slow–fast system with delayed self-coupling. In the absence of delays, this system provides a canonical example of a canard explosion. We show that as the delay is increased a family of ‘classical’ canard explosions ends as a Bogdanov–Takens bifurcation occurs at the folds points of the S-shaped critical manifold.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84940562702&origin=inward; http://dx.doi.org/10.1007/s10884-015-9478-2; http://link.springer.com/10.1007/s10884-015-9478-2; http://link.springer.com/content/pdf/10.1007/s10884-015-9478-2; http://link.springer.com/content/pdf/10.1007/s10884-015-9478-2.pdf; http://link.springer.com/article/10.1007/s10884-015-9478-2/fulltext.html; https://dx.doi.org/10.1007/s10884-015-9478-2; https://link.springer.com/article/10.1007/s10884-015-9478-2
Springer Science and Business Media LLC
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