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arXiv · 1407.7703

Canard explosion in delayed equations with multiple timescales

Maciej Krupa·Jonathan D. Touboul
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Abstract

We analyze canard explosions in delayed 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.

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Maciej Krupa, Jonathan D. Touboul. 2014-07-29. Canard explosion in delayed equations with multiple timescales. https://arxiv.org/abs/1407.7703

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