Theory and application of a nongeneric heteroclinic loop bifurcation

Homoclinic and heteroclinic bifurcations from a heteroclinic loop are consi dered. The system under consideration has three parameters, two of which ar e not suitable for generic unfoldings. Analytical criteria in terms of deri vatives to Melnikov's functions are given for nongeneric parameters. Four q ualitatively distinct bifurcation diagrams are obtained. The result is used to give an explanation of a numerical finding on the generation of traveli ng pulsing waves in a two-phase flow problem.