An iterative method to compute a closest saddle node or Hopf bifurcation instability in multidimensional parameter space

Addresses the general problem of finding bifurcations of a stable equilibrium which are closest to a given parameter vector λ₀ in a high-dimensional parameter space. The author proposes an iterative method to compute saddle node and Hopf bifurcations which are locally closest to λ₀. The iterative method extends standard, one-parameter methods of computing bifurcations and is based on formulas for the normal vector to hypersurfaces of the bifurcation set. Conditions on the hypersurface curvature are given to ensure the local convergence of the iterative method. The sensitivity to λ ₀ of the distance to a closest bifurcation is derived