A model for multiphoton excitation of a polyatomic molecule by an IR laser derived by Narducci,et al. has been analyzed by using bifurcation theory. The steady state surface formed by plotting average vibrational excitation vs laser frequency and field amplitude takes the shape of a cusp catastrophe. Linear stability analysis for a wide region in the parameter space shows that the upper branch is always stable and the middle branch unstable. The lower branch is stable for small lgr; (the ratio of the longitudinal relaxation time to the transverse one). But for large lgr; the lower branch loses stability as laser intensity increases. Analysis according to Hopfrsquo;s theorem shows that the bifurcation point is subcritical. Unstable limit cycles around the birfurcation point are found by both perturbation analysis and numerical calculations. Isotope selectivity, redhyphen;shiftedness of the optimal frequency and threshold phenomenon observed in IR multiphoton excitation of molecules can be explained in terms of this model. Practical importance of molecular bistable and hysteretic properties concerning memory devices and vibrational relaxation studies are discussed.
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