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Canard Explosion in Delay Differential Equations

Journal of Dynamics and Differential Equations, ISSN: 1572-9222, Vol: 28, Issue: 2, Page: 471-491
2016
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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.

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