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How environmental noise can contract and destroy a persistence zone in population models with Allee effect

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  • Bashkirtseva, Irina
  • Ryashko, Lev

Abstract

A problem of the analysis of the noise-induced extinction in population models with Allee effect is considered. To clarify mechanisms of the extinction, we suggest a new technique combining an analysis of the geometry of attractors and their stochastic sensitivity. For the conceptual one-dimensional discrete Ricker-type model, on the base of the bifurcation analysis, deterministic persistence zones are constructed in the space of initial states and biological parameters. It is shown that the random environmental noise can contract, and even destroy these persistence zones. A parametric analysis of the probabilistic mechanism of the noise-induced extinction in regular and chaotic zones is carried out with the help of the unified approach based on the sensitivity functions technique and confidence domains method.

Suggested Citation

  • Bashkirtseva, Irina & Ryashko, Lev, 2017. "How environmental noise can contract and destroy a persistence zone in population models with Allee effect," Theoretical Population Biology, Elsevier, vol. 115(C), pages 61-68.
    • Handle: RePEc:eee:thpobi:v:115:y:2017:i:c:p:61-68
    DOI: 10.1016/j.tpb.2017.04.001
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    1. Marten Scheffer & Steve Carpenter & Jonathan A. Foley & Carl Folke & Brian Walker, 2001. "Catastrophic shifts in ecosystems," Nature, Nature, vol. 413(6856), pages 591-596, October.
    2. Bashkirtseva, Irina & Ryashko, Lev, 2013. "Stochastic sensitivity analysis of noise-induced intermittency and transition to chaos in one-dimensional discrete-time systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 295-306.
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    Cited by:

    1. Jungeilges, Jochen & Ryazanova, Tatyana, 2019. "Transitions in consumption behaviors in a peer-driven stochastic consumer network," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 144-154.
    2. Lev Ryashko & Dmitri V. Alexandrov & Irina Bashkirtseva, 2021. "Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model," Mathematics, MDPI, vol. 9(12), pages 1-11, June.

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