Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global stabilization and destabilization by the state dependent noise
  with particular distributions   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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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin