Bistable and chaotic behavior in a damped driven Morse oscillator: A classical approach

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Abstract
Dynamical behavior of a damped Morse oscillator driven by an external sinusoidal field has been studied by solving a classical equation. Bistability of dynamical origin has been found for damping constants ranging from 0.001 to 0.4. In the weaker damping limit, corresponding to a liquid or high-pressure gas medium, bistability shows up for a large range of driving frequency and both the lower and upper branches belong to the type of period-one orbits. At the stronger damping limit, simulating a solid-state system, and in the presence of an intense field, we have found a sequence of period-doubling bifurcations leading to chaos for both the lower and upper branches. The stability diagram in the driving amplitude and frequency space show two cusp regions of bistability. This shape suggests that each of them can be described locally as a cusp catastrophe. Possible relevance of the molecular bistability to stimulated Raman scattering experiment is discussed.