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Probabilistic mechanisms of the noise-induced oscillatory transitions in a Leslie type predator-prey model

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  • Xu, Chaoqun

Abstract

A phenomenon of the noise-induced oscillatory transitions in a predator-prey model of Leslie type with generalized Holling type III functional response is studied. The original deterministic model can exhibit different kinds of phase portraits (one, two or three stable states) for various parameter values. When the predator-prey model is subjected to environmental noise, we find that the stochastic trajectory started near one of the deterministic attractors may experience the oscillatory transitions between different zones. To reveal the probabilistic mechanisms of the noise-induced transitions, we construct the confidence domains of stochastic attractors by applying the technique of stochastic sensitivity functions. It is showed that increasing the noise intensity results in an intersection between different confidence domains, and then the phenomenon of oscillatory transitions can occur.

Suggested Citation

  • Xu, Chaoqun, 2020. "Probabilistic mechanisms of the noise-induced oscillatory transitions in a Leslie type predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s096007792030271x
    DOI: 10.1016/j.chaos.2020.109871
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    1. Liao, Tiancai, 2022. "The impact of plankton body size on phytoplankton-zooplankton dynamics in the absence and presence of stochastic environmental fluctuation," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

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