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In this paper we study the stability, sensitivity, and stabilization of a stochastically perturbed Lorentz dynamical system, which represents a model of convective turbulence. The object of numerical analysis is stochastic attractors that arise in the process of self-organization of stochastic trajectories of the Lorentz system. The study is carried out using numerical simulation of the Lorenz system, perturbed by an additive stochastic differential to its right side, in the MATLAB programming environment.