Transverse Bifurcations Occurring on Simple Robust Homoclinic Cycles

This paper studies codimension-one transverse bifurcations of several classes of simple robust homoclinic cycles in group-symmetric systems on R5. The analysis follows a complete classification induced by the representation of the symmetric group. Sufficient conditions are established under which new homoclinic cycles or heteroclinic connections bifurcate from the original cycle. An asymptotic expansion of the Poincaré map is derived, yielding explicit criteria for the bifurcation of periodic orbits from such homoclinic cycles and for determining their stability.