Bulletin of Mathematical Biology

, Volume 80, Issue 6, pp 1596–1614 | Cite as

Stochastic Sensitivity Analysis of Noise-Induced Extinction in the Ricker Model with Delay and Allee Effect

  • Irina Bashkirtseva
  • Lev Ryashko
Original Article


A susceptibility of population systems to the random noise is studied on the base of the conceptual Ricker-type model taking into account the delay and Allee effect. This two-dimensional discrete model exhibits the persistence in the form of equilibria, discrete cycles, closed invariant curves, and chaotic attractors. It is shown how the Allee effect constrains the persistence zones with borders defined by crisis bifurcations. We study the role of random noise on the contraction and destruction of these zones. This phenomenon of the noise-induced extinction is investigated with the help of direct numerical simulations and semi-analytical approach based on the stochastic sensitivity functions. Stochastic transitions from the persistence regimes to the extinction are studied by the analysis of the mutual arrangement of the basins of attraction and confidence domains.


Population dynamics Noise-induced extinction Ricker-type models Allee effect Stochastic sensitivity 



The work was supported by Russian Science Foundation (N 16-11-10098).


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Ural Federal UniversityEkaterinburgRussia

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