On convergence of solutions to difference equations with additive perturbations

@article{Braverman2016OnCO,
  title={On convergence of solutions to difference equations with additive perturbations},
  author={Eric P. Braverman and Alexandra Rodkina},
  journal={Journal of Difference Equations and Applications},
  year={2016},
  volume={22},
  pages={878 - 903}
}
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can change this picture: we give examples of difference equations experiencing additive perturbations which have solutions staying around zero rather than tending to the unique positive equilibrium. When perturbations are stochastic with a bounded support, we… 
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