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Paper detail

Canard explosion in delayed equations with multiple timescales

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.

preprint2014arXivOpen access
Maciej KrupaJonathan D. Touboul
math.DS
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Maciej KrupaJonathan D. Touboul

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