Dynamical behavior of the driven Morse oscillator

Abstract

The dynamics of the driven Morse oscillator describing the photo dissociation of Molecules in theoretical chemistry was qualitatively studied. Firstly the subharmonic Melnikov method was used to prove the existence of periodic orbits in this model. Further it was rigorously proved that this model has chaotic dynamics in the sense of Smale horseshoes by introducing the famous McGehee transformation and applying the homoclinic Melnikov method. The obtained results give an analytic demonstration of the previous numerical results, that is, the driven Morse oscillator admits stochastic excitation and dissociation associated with the onset of chaos.