Nonlinear damped higher order nonlinear Schrodinger dynamics

 The spatially periodic breather solutions (SPBs)  of the nonlinear Schr\"odinger equation, prominent in modeling rogue waves, are
  unstable.
 In this paper we numerically investigate the effects of nonlinear dissipation and higher order nonlinearities  on the routes to stability of the SPBs in the 
framework of the nonlinear damped higher order nonlinear Schr\"odinger (NLD-HONLS) equation. 
We appeal to the  Floquet spectral theory of the NLS equation to interpret and provide a characterization of the perturbed dynamics in terms of nearby solutions of the NLS equation. The number of instabilities of the background Stokes wave, the damping strength, and the time of onset of  nonlinear damping  are varied. 
A broad categorization of the routes to stability of the SPBs and the novel features related to the effects of nonlinear damping will be discussed.