Codimension 3 Bifurcations Of Heteroclinic Loop Containing Two Saddle-foci

In this paper, the codimension 3 bifurcations associated with a het-eroclinic loop formed with two saddle-foci (among which, one is a weak saddle-focus) and two heterochnic orbits connecting them are studied. The existence of countably infinite 1-periodic orbits and 1(1/2)-heteroclinic orbits is given for the unperturbed system in some neighborhood of the heterochnic loop P. Meanwhile, complicated bifurcation patterns under the generic 3-paramter perturbations are also established, such as the Hopf bifurcation, 1-homoclinic bifurcation, 1-heteroclinic bifurcation,1(1/2)-heteroclinic bifurcation and coexistence of different kinds of bifurcational orbits, etc., and the numbers of the produced homoclinic or heterochnic orbits can be one, denumerable, continuum, etc.