The bifurcation diagrams for the Ginzburg–Landau system of superconductivity

In this paper, we provide the different types of bifurcation diagrams for a superconducting cylinder placed in a magnetic field along the direction of the axis of the cylinder. The computation is based on the numerical solutions of the Ginzburg–Landau model by the finite element method. The response of the material depends on the values of the exterior field, the Ginzburg–Landau parameter and the size of the domain. The solution branches in the different regions of the bifurcation diagrams are analyzed and open mathematical problems are mentioned.