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Theory and Application of a Nongeneric Heteroclinic Loop Bifurcation

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