Melnikov method

Summary

The Melnikov method is a test for whether a homoclinic orbit of a planar system survives a small periodic perturbation. It reduces the question to the zeros of one explicit integral, the Melnikov function. A simple zero of this function means that the stable and unstable manifolds of the perturbed saddle cross transversally. Such a crossing forces chaotic dynamics nearby, so the method is a standard way to prove chaos in forced oscillators. See the definition.