A pseudo-arclength continuation method for nonlinear eigenvalue problems

A variant of the classical pseudo-arclength continuation method is proposed. Basically, the method can be viewed as pseudo-arclength continuation in $(r,\lambda )$-space where r is a functional of the solution. Another difference is a three-parameter predictor instead of the standard Euler step. This predictor, as well as the Newton corrector iteration, are justified and some numerical results for reaction-diffusion equations are presented. The method provides a simple algebraic check for symmetry-breaking bifurcation, the most common type of secondary bifurcation in physical examples.