Lorenz attractors in unfoldings of homoclinic-flip bifurcations

Lorenz-like attractors are known to appear in unfoldings from certain codimension two homoclinic bifurcations for differential equations in 3 that possess a reflectional symmetry. This includes homoclinic loops under a resonance condition and the inclination-flip homoclinic loops. We show that Lorenz-like attractors also appear in the third possible codimension two homoclinic bifurcation (for homoclinic loops to equilibria with real different eigenvalues); the orbit-flip homoclinic bifurcation. We moreover provide a bifurcation analysis computing the bifurcation curves of bifurcations from periodic orbits and discussing the creation and destruction of the Lorenz-like attractors. Known results for the inclination flip are extended to include a bifurcation analysis.