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Transient Dynamics Analysis of a Predator-Prey System with Square Root Functional Responses and Random Perturbation

Author

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  • Jianguo Tan

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

  • Wenjuan Wang

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

  • Jianfeng Feng

    (Key Laboratory of Pollution Processes and Environmental Criteria, Ministry of Education, and Tianjin Key Laboratory of Environmental Remediation and Pollution Control, College of Environmental Science and Engineering, Nankai University, Tianjin 300071, China)

Abstract

In this paper, we study the asymptotic and transient dynamics of a predator–prey model with square root functional responses and random perturbation. Firstly, the mean square stability matrix is obtained from the stability theory of stochastic systems, and three stability indexes (root-mean-square resilience, root-mean-square reactivity and root-mean-square amplification envelope) of the ecosystem response to stochastic disturbances are calculated. We find that: (1) no matter which population is disturbed, increasing the intensity of disturbance improves the ability of the system leaves steady state and thus decreases the stability. The root-mean-square amplification envelope rises with increasing disturbance intensity, (2) the system is more sensitive to the disturbance of the predator than disturbance to prey, (3) ρ m a x and t m a x are important indicators, which represent the intensity and time of maximum amplification by disturbance. These findings are helpful for managers to take corresponding management measures to reduce the disturbances, especially for predators, thereby avoiding the possible change of the structure and functions of the ecosystem.

Suggested Citation

  • Jianguo Tan & Wenjuan Wang & Jianfeng Feng, 2022. "Transient Dynamics Analysis of a Predator-Prey System with Square Root Functional Responses and Random Perturbation," Mathematics, MDPI, vol. 10(21), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4087-:d:961175
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    References listed on IDEAS

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    1. Snyder, Robin E., 2010. "What makes ecological systems reactive?," Theoretical Population Biology, Elsevier, vol. 77(4), pages 243-249.
    2. Hua, Mengjiao & Wu, Yu, 2022. "Transition and basin stability in a stochastic tumor growth model with immunization," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
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    Cited by:

    1. Juan Carlos Seck-Tuoh-Mora & Joselito Medina-Marin & Norberto Hernández-Romero & Genaro J. Martínez, 2023. "Mean-Field Analysis with Random Perturbations to Detect Gliders in Cellular Automata," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
    2. Sahoo, Debgopal & Samanta, Guruprasad, 2023. "Modeling cooperative evolution in prey species using the snowdrift game with evolutionary impact on prey–predator dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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