An efficient algorithm for locating and continuing connecting orbits
  A successive continuation method for locating connecting orbits in parametrized systems of autonomous ODEs was considered in [9]. In this paper we present an improved algorithm for locating and continuing connecting orbits, which includes a new algorithm for the continuation of invariant subspaces. The latter algorithm is of independent interest, and can be used in different contexts than the present one. 
J. W. Demmel, L. Dieci, M. J. Friedman