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• W2012430741 abstract "We consider the FitzHugh-Nagumo model, an example of a system with two time scales for which Winfree was unable to determine the overall structure of the isochrons. An isochron is the set of all points in the basin of an attracting periodic orbit that converge to this periodic orbit with the same asymptotic phase. We compute the isochrons as one-dimensional parametrised curves with a method based on the continuation of suitable two-point boundary value problems. This allows us to present in detail the geometry of how the basin of attraction is foliated by isochrons. They exhibit extreme sensitivity and feature sharp turns, which is why Winfree had difficulties finding them. We observe that the sharp turns and sensitivity of the isochrons are associated with the slow-fast nature of the FitzHugh-Nagumo system; more specifically, it occurs near its repelling (unstable) slow manifold." @default.
• W2012430741 created "2016-06-24" @default.
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• W2012430741 date "2014-03-01" @default.
• W2012430741 modified "2023-10-01" @default.
• W2012430741 title "Solving Winfree's puzzle: The isochrons in the FitzHugh-Nagumo model" @default.
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• W2012430741 doi "https://doi.org/10.1063/1.4867877" @default.
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