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A remark on a stochastic logistic model with Lévy jumps

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  • Liu, Meng
  • Bai, Chuanzhi

Abstract

This note is concerned with a famous stochastic logistic equation with Lévy noises. Sufficient and necessary conditions for extinction and permanence are established. The results reveal that the Lévy noise may change the properties of population dynamics significantly. The results also reveal an important property of the Lévy noise: it is unfavorable for the permanence of the population. Some numerical simulations are introduced to validate the analytical results.

Suggested Citation

  • Liu, Meng & Bai, Chuanzhi, 2015. "A remark on a stochastic logistic model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 521-526.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:521-526
    DOI: 10.1016/j.amc.2014.11.094
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    References listed on IDEAS

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    1. Mandal, Partha Sarathi & Banerjee, Malay, 2012. "Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1216-1233.
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    Cited by:

    1. Almaz T. Abebe & Shenglan Yuan & Daniel Tesfay & James Brannan, 2024. "Most Probable Dynamics of the Single-Species with Allee Effect under Jump-Diffusion Noise," Mathematics, MDPI, vol. 12(9), pages 1-18, April.
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Asymptotic behavior of a food-limited Lotka–Volterra mutualism model with Markovian switching and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 94-104.
    3. Zhang, Xiaofeng & Yuan, Rong, 2022. "Stochastic bifurcation and density function analysis of a stochastic logistic equation with distributed delay and weak kernel," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 56-70.
    4. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Long-time behavior of a stochastic logistic equation with distributed delay and nonlinear perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 289-304.

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