Coexistence of multiple attractors, hysteresis, and vibrational resonance in the classical morse oscillator driven by an amplitude modulated signal

Abstract

We consider the classical Morse oscillator driven by an amplitude modulated signal with two widely different frequencies ω and Ω, where Ω ≫ ω. The dynamics of such oscillator is numerically studied for a specific set of parameters. We show the occurrence of coexistence of several period-T orbits, bifurcations of them, and hysteresis and vibrational resonance phenomena. We characterize the periodic and chaotic orbits, hysteresis, and vibrational resonance with the use of the bifurcation diagram and response amplitude.