  Optomechanical systems are known to exhibit a rich set of complex dynamical
features including various types of chaotic behavior and multi-stability.
Although this exotic behavior has attracted an intense research interest, the
utilization of optomechanical systems in technological applications, in most
cases necessitates a complex, yet predictable and controllable, oscillatory
response. In fact, the various types of robust oscillations supported by
optomechanical systems are nested in either the same or neighboring regions of
the parameter space, where chaos exists. In this work we systematically dissect
the parameter space of the fundamental optomechanical oscillator in order to
identify regions where stable self-sustained and self-modulated oscillations
exist, by utilizing bifurcation analysis and advanced numerical continuation
techniques. Moreover,in cases where bistability occurs, we study the
accessibility of these oscillatory states in terms of initial conditions and
their location with respect to well-defined basins of attraction. The results
provide specific knowledge for the parameter sets enabling the appropriate
oscillatory response for different types of applications.
