Canard Explosion in Delay Differential Equations |
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Authors: | Maciej Krupa Jonathan D. Touboul |
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Affiliation: | 1.MYCENAE Laboratory,Inria Paris-Rocquencourt,Paris,France;2.The Mathematical Neurosciences Laboratory,Center for Interdisciplinary Research in Biology (CNRS UMR 7241, INSERM U1050, UPMC ED 158, MEMOLIFE PSL*),Paris,France |
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Abstract: | 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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