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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, particularly dynamical systems, a heteroclinic bifurcation is a global bifurcation involving a heteroclinic cycle. Heteroclinic bifurcations come in two types, resonance bifurcations, and transverse bifurcations. Both types of bifurcation will result in the change of stability of the heteroclinic cycle. At a resonance bifurcation, the stability of the cycle changes when an algebraic condition on the eigenvalues of the equilibria in the cycle is satisfied. This is usually accompanied by the birth or death of a periodic orbit.