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• W2113751538 abstract "We investigate the organization of mixed-mode oscillations in the self-coupled FitzHugh-Nagumo system. These types of oscillations can be explained as a combination of relaxation oscillations and small-amplitude oscillations controlled by canard solutions that are associated with a folded singularity on a critical manifold. The self-coupled FitzHugh-Nagumo system has a cubic critical manifold for a range of parameters, and an associated folded singularity of node-type. Hence, there exist corresponding attracting and repelling slow manifolds that intersect in canard solutions. We present a general technique for the computation of two-dimensional slow manifolds (smooth surfaces). It is based on a boundary value problem approach where the manifolds are computed as one-parameter families of orbit segments. Visualization of the computed surfaces gives unprecedented insight into the geometry of the system. In particular, our techniques allow us to find and visualize canard solutions as the intersection curves of the attracting and repelling slow manifolds." @default.
• W2113751538 created "2016-06-24" @default.
• W2113751538 creator A5072817844 @default.
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• W2113751538 date "2008-03-01" @default.
• W2113751538 modified "2023-09-25" @default.
• W2113751538 title "Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh-Nagumo system" @default.
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• W2113751538 doi "https://doi.org/10.1063/1.2799471" @default.
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• W2113751538 hasPublicationYear "2008" @default.
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