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Coinciding local bifurcations in the Navier-Stokes equations

Generically, a local bifurcation only affects a single solution branch. However, branches that are quite different may nonetheless share certain eigenvectors and eigenvalues, leading to coincident bifurcations. For the fluidic pinball, two supercritical pitchfork bifurcations, of the equilibrium and the periodic solutions, occur at nearly the same Reynolds number. The mechanism of this kind of non-generic coincidence is modelled and explained.