Stability of equilibria of randomly perturbed maps

Abstract

We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb{R}}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on stabilization are illustrated with numerical examples of randomly perturbed linear and nonlinear maps in one- and two-dimensional spaces.

References in corpus (1)

• The Poincare map of randomly perturbed periodic motion

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• Stabilization of cycles for difference equations with a noisy PF control