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• W1992223493 abstract "A great deal of work has gone into classifying bursting oscillations,periodic alternations of spiking and quiescence modeled by fast-slowsystems. In such systems, one or more slow variables carry the fastvariables through a sequence of bifurcations that mediate transitionsbetween oscillations and steady states. A rigorous classificationapproach is to characterize the bifurcations found in the neighborhoodof a singularity; a measure of the complexity of the burstingoscillation is then given by the smallest codimension of thesingularities near which it occurs. Fold/homoclinic bursting, alongwith most other burst types of interest, has been shown to occur neara singularity of codimension three by examining bifurcations of acubic Liénard system; hence, these types of bursting have atmost codimension three. Modeling and biological considerationssuggest that fold/homoclinic bursting should be found nearfold/subHopf bursting, a more recently identified burst type whosecodimension has not been determined yet. One would expect thatfold/subHopf bursting has the same codimension as fold/homoclinicbursting, because models of these two burst types have very similarunderlying bifurcation diagrams. However, no codimension-threesingularity is known that supports fold/subHopf bursting, whichindicates that it may have codimension four. We identify athree-dimensional slice in a partial unfolding of a doubly-degenerateBodganov-Takens point, and show that this codimension-foursingularity gives rise to almost all known types of bursting." @default.
• W1992223493 created "2016-06-24" @default.
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• W1992223493 date "2012-01-01" @default.
• W1992223493 modified "2023-10-12" @default.
• W1992223493 title "Cross-currents between biology and mathematics: The codimension of pseudo-plateau bursting" @default.
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• W1992223493 doi "https://doi.org/10.3934/dcds.2012.32.2853" @default.
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