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Stationary distribution of a stochastic predator–prey model with distributed delay and general functional response

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  • Liu, Qun
  • Jiang, Daqing
  • He, Xiuli
  • Hayat, Tasawar
  • Alsaedi, Ahmed

Abstract

In this paper, we study a stochastic predator–prey model with distributed delay and general functional response. We transform the model with weak kernel case into an equivalent system through the linear chain technique. Since the diffusion matrix is degenerate, the uniform ellipticity condition does not hold. The Markov semigroup theory is used to derive the existence of a unique stable stationary distribution. We verify the densities of the distributions of the positive solutions can converge in L1 to an invariant density.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & He, Xiuli & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Stationary distribution of a stochastic predator–prey model with distributed delay and general functional response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 273-287.
    • Handle: RePEc:eee:phsmap:v:513:y:2019:i:c:p:273-287
    DOI: 10.1016/j.physa.2018.09.033
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    References listed on IDEAS

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    1. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
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    5. 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.
    6. Feng Rao, 2013. "Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, November.
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    Cited by:

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