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Analysis of a Class of Predation-Predation Model Dynamics with Random Perturbations

Author

Listed:
  • Xuewen Tan

    (Department of Mathematics, Yunnan Minzu University, No. 2929, Yuehua Street, Chenggong District, Kunming 650500, China)

  • Pengpeng Liu

    (Department of Mathematics, Yunnan Minzu University, No. 2929, Yuehua Street, Chenggong District, Kunming 650500, China)

  • Wenhui Luo

    (Department of Mathematics, Yunnan Minzu University, No. 2929, Yuehua Street, Chenggong District, Kunming 650500, China)

  • Hui Chen

    (Department of Mathematics, Yunnan Minzu University, No. 2929, Yuehua Street, Chenggong District, Kunming 650500, China)

Abstract

In this paper, we study a class of predation–prey biological models with random perturbation. Firstly, the existence and uniqueness of systematic solutions can be proven according to Lipschitz conditions, and then we prove that the systematic solution exists globally. Moreover, the article discusses the long-term dynamical behavior of the model, which studies the stationary distribution and gradual properties of the system. Next, we use two different methods to give the conditions of population extinction. From what has been discussed above, we can safely draw the conclusion that our results are reasonable by using numerical simulation.

Suggested Citation

  • Xuewen Tan & Pengpeng Liu & Wenhui Luo & Hui Chen, 2022. "Analysis of a Class of Predation-Predation Model Dynamics with Random Perturbations," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3238-:d:908325
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    References listed on IDEAS

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    1. Viktor Stojkoski & Trifce Sandev & Ljupco Kocarev & Arnab Pal, 2021. "Geometric Brownian Motion under Stochastic Resetting: A Stationary yet Non-ergodic Process," Papers 2104.01571, arXiv.org, revised Aug 2021.
    2. Guirong Liu & Sanhu Wang & Jurang Yan, 2011. "Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-14, July.
    3. Zhang, Wei & Yin, Xunbo & Song, M.H. & Liu, M.Z., 2019. "Convergence rate of the truncated Milstein method of stochastic differential delay equations," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 263-281.
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