A direct method for the numerical computation of bifurcation points underlying symmetries

A direct method for the numerical computation of pitchfork bifurcation points under certain symmetry conditions is presented. We will be interested in computing the critical parameter. The direct method presented produces a larger system of full rank and hence solvable. The presence of symmetry will be of help since it will reduce the amount of work needed. Numerical experimentation will be done to demonstrate the efficiency of the suggested approach.