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• W2794093354 abstract "Canard orbits are relevant objects in slow-fast dynamical systems that organize the spiraling of orbits nearby. In three-dimensional vector fields with two slow and one fast variables, canard orbits arise from the intersection between an attracting and a repelling two-dimensional slow manifold. Special points called folded nodes generate such intersections: in a suitable transverse two-dimensional section Σ, the attracting and repelling slow manifolds are counter-rotating spirals that intersect in a finite number of points. We present an implementation of Lin's method that is able to detect all of these intersection points and, hence, all of the canard orbits arising from a folded node. With a boundary-value-problem setup we compute orbit segments on each slow manifold up to Σ, where we require that the corresponding end points in Σ lie in a one-dimensional subspace known as the Lin space Z. The Lin space Z must be transverse to the slow manifolds and it remains fixed during the detection of canard orbits as zeros of the signed distance along Z. During the computation, a tangency of Z with one of the intersection curves in Σ may arise. To overcome this, we update the Lin space at an intermediate continuation step to detect a double tangency of Z to both curves in Σ, after which the canard detection is able to continue. Our method is demonstrated with the examples of the normal form for a folded node and of the Koper model." @default.
• W2794093354 created "2018-03-29" @default.
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• W2794093354 creator A5072817844 @default.
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• W2794093354 date "2017-01-01" @default.
• W2794093354 modified "2023-09-26" @default.
• W2794093354 title "A Lin's method approach for detecting all canard orbits arising from a folded node" @default.
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• W2794093354 doi "https://doi.org/10.3934/jcd.2017005" @default.
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