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We consider an effect of random disturbances on the generalized logistic model with delay in mono- and bistable regimes near Neimark–Sacker bifurcation. Noise-induced transitions between coexisting attractors, and between separate parts of the unique attractor, are studied. We suggest a semi-analytical approach that combines a geometric analysis of the mutual arrangement of attractors, their basins of attraction, and corresponding confidence domains found by the stochastic sensitivity functions technique. Constructive abilities of this approach are demonstrated for the generalized logistic model with delay.

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We study the dynamics of stochastically forced 2D logistic-type discrete model. Under random disturbances, stochastic trajectories leaving deterministic attractors can form complex dynamic regimes that have no analogue in the deterministic case. In this paper, we analyze an impact of the random noise on 2D logistic-type model in the bistability zones with coexisting attractors (equilibria, closed invariant curves, discrete cycles). For the constructive probabilistic analysis of the random states distribution around such attractors, a stochastic sensitivity functions technique and method of confidence domains are used. For the considered model, on the base of the suggested approach, a phenomenon of noise-induced transitions between attractors and the generation of chaos are analyzed.