Abstract
Abstract The problem addressed is to construct a feedback regulator that stabilizes an equilibrium of the randomly forced nonlinear dynamic system, and synthesizes a required stochastic sensitivity of this equilibrium. The aim of this paper is to demonstrate how elaborated control theory can be used for the protection of the ecological systems against catastrophic shifts. In present paper, a stochastically forced predator-prey model with Allee effect is studied. A probabilistic mechanism of the noise-induced extinction of both species is shown. Using stochastic sensitivity functions technique, we construct confidence ellipses and estimate the threshold value of the intensity for noise generating a transition from the stable coexistence of both species to the extinction. For the stabilization of this population system, a method of the control for confidence ellipses is applied. It is shown that the regulator provides a low level of stochastic sensitivity and prevents unwanted ecological catastrophes.
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