Discretized Fast-Slow Systems with Canard Points in Two Dimensions
We study the behaviour of slow manifolds for two different discretization schemes of fast-slow systems with canard fold points. The analysis uses the blow-up method to deal with the loss of normal hyperbolicity at the canard point. While the Euler method does not preserve the folded canard, we can show that the Kahan discretization allows for a similar result as in continuous time, guaranteeing the occurence of canard connections between attracting and repelling slow manifolds upon variation of a bifurcation parameter. Furthermore, we investigate the existence and properties of a formal conserved quantity in the rescaled Kahan map.
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Maximilian Engel (edit)
Christian Kuehn (add twitter)
Matteo Petrera (add twitter)
Yuri Suris (add twitter)
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Mathematics - Dynamical Systems

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07/15/19 06:02PM
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mathDSb: Maximilian Engel, Christian Kuehn, Matteo Petrera, Yuri Suris : Discretized Fast-Slow Systems with Canard Points in Two Dimensions https://t.co/lQDCGM9Qmp https://t.co/yL77YUaSQx
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