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Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic Dynamics

Research output: Contribution to journalArticle

Original languageEnglish
Article number1950157
Number of pages10
JournalInternational Journal of Bifurcation and Chaos
Issue number11
DateAccepted/In press - 10 May 2019
DatePublished (current) - 1 Oct 2019


We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the "Morse oscillator"). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of time, their period for the bounded trajectories, and action-angle variables. We use these trajectories to prove sufficient conditions for chaotic dynamics, in the sense of Smale horseshoes, for the time-periodically perturbed Morse oscillator using a Melnikov type approach.

    Research areas

  • chaos, Melnikov function, homoclinic orbit, action-angle variables, Morse oscillator



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