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This article is devoted to the research of a new codimension 3 homoclinic orbit bifurcation, which is the orbit-flip of weak type. Such kind of homoclinic orbit is a degenerate case of the orbit-flip homoclinic orbit. We show the existence of 1homoclinic orbit, 1-periodic orbit, 2n-homoclinic orbit and 2n-periodic orbit for arbitrary integer n. Our strategy is based on the local moving coordinates method.

Codimension 3 bifurcation from orbit-flip homoclinic orbit of weak type