Optomechanical systems are known to exhibit self-sustained limit cycles once driven above the parametric instability point. This breaks down the linearized approximation and induces novel nonlinear effects such as dynamical multistability, staircase behavior, and the generation of optical high-order sideband combs (HOSCs). Here, we study the classical nonlinear dynamics of optomechanical systems. We combine numerical simulations and analytical investigation to predict dynamical multistability in the resolved sideband regime. A way to predict the onset of the period doubling process and to control the multistability is analytically provided by tuning the optical linewidth. Indeed, the multistability behavior first changes to a staircase shape and gradually disappears as the system approaches the unresolved sideband limit. We exploit the multistable attractors to generate optical HOSCs by acting solely on the initial values instead of increasing the driving strength. This is the figure of merit of our proposal to relate multistability to the HOSC. As a result, the properties (bandwidth, intensity) of the combs are improved as the mechanical resonator moves towards upper attractors. This work opens a way for low-power HOSC generation in optomechanics and the related technological applications.
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