Homoclinic bifurcation is a phenomenon in dynamical systems where a system undergoes a qualitative change due to the intersection of stable and unstable manifolds of a saddle point. This intersection creates homoclinic orbits, which are trajectories that return to the same saddle point after some time. This type of bifurcation is crucial in understanding the complex behavior of systems, as it often leads to chaotic dynamics and changes in the stability of equilibria.
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