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About asymptotic properties of bilinear difference equations under stochastic perturbations
  • Leonid Shaikhet
Leonid Shaikhet
Ariel University

Corresponding Author:[email protected]

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Abstract

Rational bilinear difference equations are very popular in research. In this paper the asymptotic properties of a rational bilinear difference equation are studied under stochastic perturbations. It is assumed that stochastic perturbations are proportional to the deviation of the current value of the equation solution from one of its equilibria (the zero or nonzero). Some conditions are obtained under which the considered equilibrium is stable in probability or unstable. The obtained results are illustrated by numerical simulation of solutions of the considered stochastic difference equation. It is noted that the research method used here can be applied to study many other types of nonlinear difference equations. To readers attention some unsolved problem of stabilization by noise for stochastic difference equations is also proposed.