We consider a singularly perturbed system with two normally hyperbolic centre manifolds. We derive a first bifurcation function, the zeros of which correspond 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.
Heteroclinic Connections in Singularly Perturbed Systems / Battelli, Flaviano; Palmer, K. J.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - 9:(2008), pp. 431-481.