Codimension-one bifurcation classification conjecture for one-fast, two-slow critical sets
Codimension-one bifurcation classification conjecture for one-fast, two-slow critical sets
Let define a critical set for a system with one fast variable and two slow variables. Let denote the listed degeneracy subsets, with a slow-variable value.
Codimension-one bifurcation conjecture. The codimension-one bifurcations of critical sets are characterised by the stated classification: precisely one set is non-empty, for precisely one , and precisely one of the following occurs: a loop or pair of hyperbolae appears in the fold projections at a fold tangency ; two cusps annihilate at a cusp tangency ; a quadratic fold line folds over to form two cusps in a swallowtail ; the projections of two quadratic fold curves become tangent at ; the projections of a quadratic fold curve and a cubic cusp intersect at ; or the projections of three fold lines intersect at .
This is a proposed classification of codimension-one bifurcations in the one-fast, two-slow case, analogous to the preceding one-fast, one-slow classification. The source provides no evidence that the classification has been proved or refuted.
Sources & referencesView supporting material
Primary source
Karl Nyman, Peter Ashwin and Peter Ditlevsen, “Bifurcation of critical sets and relaxation oscillations in singular fast-slow systems”, arXiv:1902.09203 (2019).
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