A Note on Bifurcation of Equilibrium Forms of a Gas Balloon Parachute

We will be concerned with deformations of a free elastic top rim of a parachute of a gas balloon. The top rim is connected with the circular deflation port of the balloon envelope by heavy duty flexible load tapes. The inside part of the balloon is filled with compressed gas. Equilibrium forms of the parachute may be found as solutions of a certain nonlinear functional-differential equation with two physical parameters: an elasticity coefficient of tapes and a physical parameter describing compressed gas. This equation possesses radially symmetric solutions corresponding to circular shapes of the top rim. Our goal is to study the existence of symmetry breaking bifurcation of the top rim of parachute.