Heteroclinic connections in singularly perturbed systems

We consider a singularly perturbed system with two normally hyperbolic centre manifolds. We derive one bifurfation function, the zeros of which corrspond to heteroclinic connections near such a connection for the unperturbed system, and a second bifurcation function the zeros of which correspond to the vectors in the intersection of the tangent spaces to the centre unstable and centre-stable manifolds along the heteroclinic connections.