Symmetry-breaking bifurcations for free elastic shell of biological cluster

Considered is a two-dimensional mathematical model for free elastic exterior shell of a biological cluster. The cluster shell is connected with cluster kernel by elastic links. The inside part is filled by compressed gas or fluid. The nonlinear functional-differential equation describing the form of shell has been obtained using variational principle and contains several physical parameters. For each parameter value this equation has a radial symmetry solution. Our goal is to identify the bifurcation which breaks the symmetry. The critical values of bifurcation parameter and buckling modes are found by considering the linearised problem. The nonlinear model is reduced to operator equation with Fredholm type operator of index 0. The Crandall-Rabinovitz bifurcation theorem (gradient case) is used to prove the bifurcation theorem.