  There is a recent development in the carrying simplex theory for competitive
maps: under some weaker conditions a map has a modified carrying simplex (one
of the author's latest publications). In this paper, as one of the applications
of the modified carrying simplex theory, a criterion is established for a three
dimensional Kolmogorov map to have a globally repelling (attracting)
heteroclinic limit cycle. As a concrete example, a discrete competitive model
is investigated to illustrate the above criteria for global repulsion
(attraction) of a hetericlinic limit cycle.
