Effective Hamiltonian for chaotic coupled oscillators

A generalized effective fitting Hamiltonian is tested against a model system of highly excited coupled Morse oscillators. At energies approaching dissociation, a very few resonance couplings in addition to the standard 1:1 and 2:2 couplings of the Darling-Dennison Hamiltonian suffice to fit the spectrum and match the large-scale features of the mixed regular and chaotic phase spaces, consisting of resonance zones organized around periodic orbits of low order that break the total polyad action.