Computation of bifurcation manifolds of linearly independent homoclinic orbits

Regarding the small perturbation as a parameter in an appropriate space of functions, we can discuss co-existence of homoclinic orbits for non-autonomous perturbations of an autonomous system in and describe conditions of parameters for such degenerate homoclinic bifurcations with some bifurcation manifolds of infinite dimension. Since those manifolds determine the relation among parameters for such bifurcations, in this paper we give an algorithm to compute approximately those manifolds and concretely obtain their first order approximates.