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Analysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model

Author

Listed:
  • Wen Liu

    (School of Mathematical Sciences, Tiangong University, Tianjin 300387, China)

  • Jianfeng Feng

    (School of Mathematical Sciences, Tiangong University, Tianjin 300387, China)

Abstract

In this paper, we focus on the asymptotic and transient dynamics of the studied ecosystem and measure the response to perturbation of the stochastic ratio-dependent predator–prey model. The method we use is mainly based on the Kronecker product and numerical simulation. Firstly, the mean-square stability matrix can be calculated from the Kronecker product, so as to compute three indicators (root-mean-square resilience, root-mean-square reactivity and root-mean-square amplification envelope) of the response to perturbation for the studied ecosystem. Since the above-measured amounts cannot be obtained explicitly, we use numerical simulation to draw the changing figures within the appropriate parameter range. Then we obtain some conclusions by comparing the numerical results. When perturbing any populations, increasing the disturbance intensity will reduce the mean-square stable area of the system. Ecologists can manage the ecosystem, reduce losses and maximize benefits according to the numerical results of the root-mean-square amplification envelope.

Suggested Citation

  • Wen Liu & Jianfeng Feng, 2021. "Analysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model," Mathematics, MDPI, vol. 9(21), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2776-:d:670347
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    References listed on IDEAS

    as
    1. Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Dynamical Behavior of a Stochastic Ratio-Dependent Predator-Prey System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, May.
    2. Junli Liu & Pan Lv & Bairu Liu & Tailei Zhang & Eulalia Martinez, 2021. "Dynamics of a Predator-Prey Model with Fear Effect and Time Delay," Complexity, Hindawi, vol. 2021, pages 1-16, April.
    3. Snyder, Robin E., 2010. "What makes ecological systems reactive?," Theoretical Population Biology, Elsevier, vol. 77(4), pages 243-249.
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