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arXiv · 2002.12472

Global stabilization and destabilization by the state dependent noise with particular distributions

Elena Braverman·Alexandra Rodkina
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Abstract

Under natural assumptions, an unstable equilibrium of a difference equation can be stabilized by a bounded multiplicative noise, identically distributed at each step. This includes stabilization of an otherwise unstable positive equilibrium of Ricker, logistic, and Beverton-Holt maps. Introduction of a multiplicative noise also allows to destabilize a stable equilibrium in a sense that all solutions stay away from this point, almost surely. In our examples a noise has symmetric, discrete or continuous, distribution with support $[-1,1]$, including Bernoulli and uniform continuous distribution. We obtain conditions on the noise amplitudes in each case that allow to either stabilize or destabilize an equilibrium. Computer simulations illustrate our results.

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Elena Braverman, Alexandra Rodkina. 2020-02-27. Global stabilization and destabilization by the state dependent noise with particular distributions. https://doi.org/10.1016/j.physd.2019.132302

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