Global Bifurcations and their Numerical Computation

Global bifurcations in dynamical systems often occur from homoclinic or heteroclinic orbits. The best known effect is the termi-nation of a branch of periodic orbits at a homoclinic orbit. In this paper we extend our numerical approach to connecting orbits and the error analysis developed in [1]. The basic nondegeneracy condition is characterized by a geometric transversality condition. Further, the analysis of the error obtained by truncating to a finite interval is generalized in order to include periodic boundary conditions and to explain the superconvergence phenomenon with respect to the parameter as observed in [1].