Direction of branches bifurcating at a bifurcation point. determination of starting points for a continuation algorithm

摘要

The behavior of branches of solutions of a system of nonlinear algebraic equations depending on a parameter in a neighborhood of a bifurcation point is examined. Directions of branches emanating from the bifurcation point are computed, and starting points for a continuation algorithm are suggested on the basis of these directions. Results for three examples are shown, and a case with higher degeneracy is discussed.