Parabolic bursting, spike-adding, dips and slices in a minimal model

Abstract : A minimal system for parabolic bursting, whose associated slow flow is integrable, is presented and studied both from the viewpoint of bifurcation theory of slow-fast systems, of the qualitative analysis of its phase portrait and of numerical simulations. We focus the analysis on the spike-adding phenomenon. After a reduction to a periodically forced 1-dimensional system, we uncover the link with the dips and slices first discussed by J. E. Littlewood in his famous articles on the periodically forced van der Pol system.
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https://hal.inria.fr/hal-01911267
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Submitted on : Friday, November 2, 2018 - 3:56:52 PM
Last modification on : Friday, April 19, 2019 - 4:54:57 PM
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  • HAL Id : hal-01911267, version 1

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Mathieu Desroches, Jean-Pierre Françoise, Martin Krupa. Parabolic bursting, spike-adding, dips and slices in a minimal model. 2018. ⟨hal-01911267⟩

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