Stochastic Sensitivity Analysis and Control for Ecological Model with the Allee Effect

In this paper, we discuss a problem of the analysis and prevention of catastrophic shifts in ecosystems with stochastic environment. For the solution of this problem in models of ecological dynamics, a new approach based on the stochastic sensitivity functions technique is suggested and applied to a stochastically forced predator-prey model with the Allee effect. For this population model, we analyze a phenomenon of noise-induced extinction using the method of confidence domains. By controlling those domains we provide a stable coexistence of both species and prevent the noise-induced extinction.