Stochastic Control in the Problem of Preventing Ecological Catastrophes

Abstract

A problem of the analysis and prevention of catastrophic shifts in stochastically forced ecosystems is considered. For the solution of this problem, a new mathematical approach based on the analysis and synthesis of the stochastic sensitivity of dynamic regimes in population models is suggested. Technical details of this approach are discussed for the conceptual stochastically forced Bazykin-Berezovskaya predator-prey model with the Allee effect. For this population model, a phenomenon of the noise-induced extinction is analysed by the method of confidence domains. By reducing these domains we provide a stabilization of the persistence regime for both interacting species. © 2018