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- W1880775923 abstract "Numerical studies indicate that the FitzHugh--Nagumo system exhibits stable traveling pulses with oscillatory tails. In this paper, the existence of such pulses is proved analytically in the singular perturbation limit near parameter values where the FitzHugh--Nagumo system exhibits folds. In addition, the stability of these pulses is investigated numerically, and a mechanism is proposed that explains the transition from single to double pulses that was observed in earlier numerical studies. The existence proof utilizes geometric blow-up techniques combined with the exchange lemma: the main challenge is to understand the passage near two fold points on the slow manifold where normal hyperbolicity fails." @default.
- W1880775923 created "2016-06-24" @default.
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- W1880775923 date "2015-01-01" @default.
- W1880775923 modified "2023-10-16" @default.
- W1880775923 title "Fast Pulses with Oscillatory Tails in the FitzHugh--Nagumo System" @default.
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- W1880775923 doi "https://doi.org/10.1137/140999177" @default.
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