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Dynamics of a Stochastic Predator-Prey System in Presence of Competitor for Prey with Fear Effect and Hunting Cooperation

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  • Debasis Mukherjee

    (Vivekananda College)

Abstract

This paper studies a stochastic predator-prey model in presence of competitor for the prey. Here, one of the competing prey species is affected by the fear of predators while the other competing prey species is not consumed by the predators nor even attacked. The deterministic model without hunting cooperation is already analyzed. The impact of considering hunting cooperation on the system dynamics is indicated. For the stochastic model, the existence of a unique global positive solution and ultimate boundedness are investigated. The asymptotic mean square stability of the predator free equilibrium point is examined. The results obtained are verified through numerical simulations.

Suggested Citation

  • Debasis Mukherjee, 2025. "Dynamics of a Stochastic Predator-Prey System in Presence of Competitor for Prey with Fear Effect and Hunting Cooperation," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-15, June.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10167-5
    DOI: 10.1007/s11009-025-10167-5
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    References listed on IDEAS

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    1. Debasis Mukherjee, 2022. "Stochastic Analysis of an Eco-Epidemic Model with Biological Control," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2539-2555, December.
    2. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
    3. Mukherjee, Debasis, 2020. "Role of fear in predator–prey system with intraspecific competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 263-275.
    4. Li, Haihong & Cong, Fuzhong, 2019. "Dynamics of a stochastic Holling–Tanner predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    5. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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