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Dynamic properties for a stochastic food chain model

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  • Zou, Xiaoling
  • Ma, Pengyu
  • Zhang, Liren
  • Lv, Jingliang

Abstract

In this paper, Lyapunov exponents of ergodic invariant measures are used to study dynamic properties for a stochastic food chain model, which consists of two competing predators and one prey. Ayala’s experimental result, or rather, competitive coexistence is showed to be possible in this random case. Furthermore, the considered stochastic model have five points of dynamical bifurcation, which happen to be the thresholds (between survival and extinction) of the system or each species. In addition, the necessity of introducing environmental noise is verified by the fact that environmental driving force can drive the system towards extinction from partial extinction or coexistence. Moreover, all the theoretical results are well verified by numerical simulations. It is worth mentioning that we make a first attempt at using meshing method and statistical data to test Lyapunov exponents for two-dimensional boundary measures, and this is an innovation in the numerical methods.

Suggested Citation

  • Zou, Xiaoling & Ma, Pengyu & Zhang, Liren & Lv, Jingliang, 2022. "Dynamic properties for a stochastic food chain model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010675
    DOI: 10.1016/j.chaos.2021.111713
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    References listed on IDEAS

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    1. Zhao, Dianli & Yuan, Sanling, 2016. "Dynamics of the stochastic Leslie–Gower predator–prey system with randomized intrinsic growth rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 419-428.
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    6. Zhongwei Cao & Qiumei Zhang & Yanan Zhao, 2018. "The Principle of Competitive Exclusion about a Stochastic Lotka-Volterra Model with Two Predators Competing for One Prey," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-13, July.
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    Cited by:

    1. Zou, Xiaoling & Li, Qingwei & Cao, Wenhao & Lv, Jingliang, 2023. "Thresholds and critical states for a stochastic predator–prey model with mixed functional responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 780-795.

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