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 one-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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Submitted on : Friday, November 2, 2018 - 3:56:52 PM
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Mathieu Desroches, Jean-Pierre Françoise, Martin Krupa. Parabolic bursting, spike-adding, dips and slices in a minimal model. Mathematical Modelling of Natural Phenomena, EDP Sciences, 2019, Mathematical Modelling of Natural Phenomena (MMNP), ⟨10.1051/mmnp/2019018⟩. ⟨hal-01911267⟩

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