Continuation Methods and Disjoint Equilibria

Continuation methods are efficient to trace branches of fixed point solutions in parameter space as long as these branches are connected. However, the computation of isolated branches of fixed points is a crucial issue and require ad-hoc techniques. We suggest a modification of the standard continuation methods to determine these isolated branches more systematically. The so-called residue continuation method is a global homotopy starting from an arbitrary disjoint initial guess. Explicit conditions ensuring the quadratic convergence of the underlying Newton-Raphson process are derived and illustrated through several examples.