Sadakathullah Appa College, India

The nonlinear vibrational dynamics of anharmonic molecules under external fields are investigated using a damped Morse oscillator subjected to multi-frequency excitation. The Morse potential provides a realistic model for molecular bond vibrations, enabling the study of vibrational stability and chaos in driven molecular systems. Analytical threshold conditions for the onset of homoclinic chaos are derived using the Melnikov method for both linear and nonlinear damping. Numerical simulations reveal diverse dynamical regimes, including periodic, quasi-periodic, reverse period-doubling, periodic bubble, antimonotonic, and chaotic motions. The interplay between multiple driving frequencies strongly influences the transition between regular and chaotic dynamics, while the forcing amplitudes and damping strengths serve as effective control parameters. Comparison of linear and nonlinear damping demonstrates their distinct roles in energy dissipation and the routes to chaos. These results provide new insights into the nonlinear response of anharmonic molecular vibrations under multifrequency excitation and suggest potential strategies for controlling vibrational energy localization and laser-driven molecular excitation. Keywords: Morse oscillator; Anharmonic molecular vibrations; Multifrequency excitation; Nonlinear damping; Homoclinic chaos.