Abstract
The computation of symmetry-breaking bifurcation points of nonlinear multiparameter problems with$Z_2 $ (reflectional) symmetry is considered. The numerical approach is based on recent work in singularity theory, which is used to construct systems of equations and inequalities characterising various types of symmetry-breaking bifurcation points. Numerical continuation methods are then used to follow paths of symmetry-breaking bifurcations, and hence compute regions in parameter space for which a problem has qualitatively similar bifurcation diagrams. The power of the numerical approach is illustrated by computations of axisymmetric flows in the finite Taylor problem.
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