# 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}
}
• Published 25 March 2016
• Mathematics
• Journal of Difference Equations and Applications
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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## References

SHOWING 1-10 OF 16 REFERENCES
Constrained stability and instability of polynomial differenceequations with state-dependent noise
• Mathematics
• 2009
We examine the stability and instability of solutions of a polynomial difference equation with state-dependent Gaussian perturbations, and describe a phenomenon that can only occur in discrete
Non-exponential stability and decay rates in nonlinear stochastic difference equations with unbounded noise
• Mathematics
• 2009
We consider the stochastic difference equation where f and g are nonlinear, bounded functions, is a sequence of independent random variables, and h>0 is a nonrandom parameter. We establish results on
On stochastic stabilization of difference equations
• Mathematics
• 2006
We consider unstable scalar deterministic difference equation $x_{n+1}=x_n(1+a_nf(x_n))$, $n\ge 1$, $x_0=a$. We show how this equation can be stabilized by adding the random noise term
Stabilization of two cycles of difference equations with stochastic perturbations
• Mathematics, Physics
• 2013
A map which experiences a period doubling route to chaos, under a stochastic perturbation with a positive mean, can have a stable blurred two-cycle for large enough values of the parameter. The limit
Random perturbations of difference equations with Allee effect: switch of stability properties
For difference equations with the Allee effect, small initial values lead to extinction, while large enough values ensure survival. However, even a scarce (applied not every step) random perturbation
Local stabilization of abstract discrete-time systems
In this paper, local stabilization for semi-linear abstract difference systems is considered. Specifically, we study the semi-linear difference system , , where are bounded linear operators acting on
Global stabilization in nonlinear discrete systems with time-delay
• Mathematics
J. Glob. Optim.
• 2013
The existence of optimal solutions is established and their stability (the turnpike property) is proved.
On the oscillation of solutions of stochastic difference equations
• Mathematics
• 2007
Resumen en: This paper considers the pathwise oscillatory behaviour of the scalar nonlinear stochastic difference equation X(n + 1) = X(n) - F(X(n)) + G(n,X(n))E(n +...