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Dynamics of a Stochastic Predator–Prey Model with Smith Growth Rate and Cooperative Defense

Author

Listed:
  • Qiuyue Zhao

    (School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China)

  • Xinglong Niu

    (School of Electrical and Control Engineering, North University of China, Taiyuan 030051, China)

Abstract

The random changes in the environment play a crucial role in the sustainability of ecosystems. Usually, the construction of stochastic models does not take into account the non-linear growth of intrinsic growth rate. In addition, prey only considers the collective response of the population when encountering predators and ignores the role of individual prey. To address this issue, we contemplate the dynamics of a stochastic prey–predator model with Smith growth rate and cooperative defense. The population density of prey is measured by mass, and the growth limitations are based on the proportion of unused available resources. Additionally, the grazing pattern of the predator incorporates cooperative characteristics into the functional response. We carry out existence and uniqueness analysis for the global positive solution. Then, we construct sufficient conditions for the existence of an ergodic stationary distribution of positive solutions for investigating whether prey and predator populations continue to survive. Numerical examples indicate that the Smith growth rate, cooperative defense and environmental disturbance play crucial roles in the coexistence of interacting populations.

Suggested Citation

  • Qiuyue Zhao & Xinglong Niu, 2024. "Dynamics of a Stochastic Predator–Prey Model with Smith Growth Rate and Cooperative Defense," Mathematics, MDPI, vol. 12(12), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1796-:d:1411524
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    References listed on IDEAS

    as
    1. Zhao, Shengnan & Yuan, Sanling & Zhang, Tonghua, 2022. "The impact of environmental fluctuations on a plankton model with toxin-producing phytoplankton and patchy agglomeration," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Feng, Xiaozhou & Liu, Xia & Sun, Cong & Jiang, Yaolin, 2023. "Stability and Hopf bifurcation of a modified Leslie–Gower predator–prey model with Smith growth rate and B–D functional response," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
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