Symmetry breaking and the twisted elastic ring Original Research Article

Symmetry breaking is considered in the context of a parameter-dependent two-point boundary value problem describing a twisted elastic ring that arises as a model of DNA minicircles. We explicitly determine, via a perturbation expansion, those representatives of a manifold of solutions to a symmetric BVP that persist when the symmetry is broken. Conditions generating a generic splitting are identified, and some degenerate cases are studied. In both the generic and degenerate cases, the results of the perturbation expansion are used to improve the efficiency of existing algorithms for computing symmetry-broken bifurcation diagrams.