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Analysis of a stochastic logistic model with diffusion

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  • Liu, Meng
  • Deng, Meiling
  • Du, Bo

Abstract

Taking both white noise and Lévy jump noise into account, a stochastic logistic model with diffusion is proposed and considered. Under some simple assumptions, the almost complete parameters analysis of the model is carried out. In each case it is shown that the population in each patch is either stable in time average or extinct, depending on the parameters of the model, especially, depending on the intensity of the Lévy jump noise. Some simulation figures are introduced to validate the theoretical results.

Suggested Citation

  • Liu, Meng & Deng, Meiling & Du, Bo, 2015. "Analysis of a stochastic logistic model with diffusion," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 169-182.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:169-182
    DOI: 10.1016/j.amc.2015.05.050
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    References listed on IDEAS

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    1. Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(2), pages 231-247, August.
    2. Kunita, Hiroshi, 2010. "Itô's stochastic calculus: Its surprising power for applications," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 622-652, May.
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    Cited by:

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    2. Xiangjun Dai & Hui Jiao & Jianjun Jiao & Qi Quan, 2023. "Survival Analysis of a Predator–Prey Model with Seasonal Migration of Prey Populations between Breeding and Non-Breeding Regions," Mathematics, MDPI, vol. 11(18), pages 1-19, September.
    3. Ayoubi, Tawfiqullah & Bao, Haibo, 2020. "Persistence and extinction in stochastic delay Logistic equation by incorporating Ornstein-Uhlenbeck process," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. Wang, Sheng & Wang, Linshan & Wei, Tengda, 2018. "Permanence and asymptotic behaviors of stochastic predator–prey system with Markovian switching and Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 294-311.
    5. Sheng Wang & Linshan Wang & Tengda Wei, 2017. "Well-Posedness and Asymptotic Behaviors for a Predator-Prey System with Lévy Noise," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 715-725, September.
    6. Wang, Sheng & Hu, Guixin & Wei, Tengda & Wang, Linshan, 2020. "Permanence of hybrid competitive Lotka–Volterra system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

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