2 problems

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McCalla–Sandstede conjecture on collapse of the upper snaking branch
Consider the upper snaking branch of localized axisymmetric patterns, whose spatially periodic patches (SPPs) are added near the core of the pattern, namely near $r=0$ , rather than…
Conjectureopenbifurcation-theory localized-patterns snakingarXiv posted 2 days ago
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The exponentially narrow snaking conjecture for cold connecting branches
Let the cold hexagons, cold stripes, and the homogeneous solution be the associated patterns connected by the observed cold connecting branches. Their Ginzburg--Landau energies det…
Conjectureopenpattern-formation reaction-diffusion snakingarXiv posted 2 days ago

McCalla–Sandstede conjecture on collapse of the upper snaking branch