Bifurcations with spherical symmetry - Sigrist, Rachel (2010)
Bifurcations from spherically symmetric states can occur in many physical and biological systems. These include the development of a spherical ball of cells into an asymmetrical state and the buckling of a sphere under pressure. They also occur in the evolution of reaction–diffusion systems on a spherical surface and in Rayleigh–Benard convection in a spherical shell. Many of the behaviours of these systems can be explained by their underlying spherical symmetry alone. Using results from the area of mathematics known as equivariant bifurcation theory we can use group theoretical methods both to predict the symmetries of the solutions which are expected to result from bifurcations with symmetry and compute their stability. In this thesis both stationary and Hopf bifurcation with spherical symmetry are discussed.