Crises, noise, and tipping in the Hassell population model.

We consider a problem of the analysis of the noise-induced tipping in population systems. To study this phenomenon, we use Hassell-type system with Allee effect as a conceptual model. A mathematical investigation of the tipping is connected with the analysis of the crisis bifurcations, both boundary and interior. In the parametric study of the abrupt changes in dynamics related to the noise-induced extinction and transition from order to chaos, the stochastic sensitivity function technique and confidence domains are used. The effectiveness of the suggested approach to detect early warnings of critical stochastic transitions is demonstrated.