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A prey–predator model with refuge for prey and additional food for predator in a fluctuating environment

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  • Das, Amartya
  • Samanta, G.P.

Abstract

Refuge for prey and additional food for predator together with environmental fluctuation is a very interesting topic for dynamical system. In this work we have studied a prey–predator model in presence of some additional food to predators and incorporating refuge for prey which protects certain amount of prey. In this model prey grows logistically in absence of predator. Functional response of predator towards additional food and prey is derived considering mutual interference among the individuals of the predator. We have introduced Gaussian white noise to model the influence of environmental fluctuations on the growth rate of prey and the death rate of predator. We have shown, how Gaussian white noise plays an important role for extinction and persistence of the system. Some important properties such as positivity, boundedness, uniform continuity etc. of the solution are proved. In extinction scenario we have found that extinction of prey population propel predator population to extinct. It is considered that prey refuge depends on biomass of prey and predator population both. In numerical simulation we have justified how this consideration is more actual to the reality. Also it is shown the importance of additional food to predator as prey may not be available (prey may get refuge) for predation.

Suggested Citation

  • Das, Amartya & Samanta, G.P., 2020. "A prey–predator model with refuge for prey and additional food for predator in a fluctuating environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    • Handle: RePEc:eee:phsmap:v:538:y:2020:i:c:s0378437119316188
    DOI: 10.1016/j.physa.2019.122844
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    References listed on IDEAS

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    1. 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.
    2. Manna, Debasis & Maiti, Alakes & Samanta, G.P., 2018. "Analysis of a predator-prey model for exploited fish populations with schooling behavior," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 35-48.
    3. Mondal, Sudeshna & Samanta, G.P., 2019. "Dynamics of an additional food provided predator–prey system with prey refuge dependent on both species and constant harvest in predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    4. Das, Amartya & Samanta, G.P., 2018. "Stochastic prey–predator model with additional food for predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 121-141.
    5. Ghosh, Joydev & Sahoo, Banshidhar & Poria, Swarup, 2017. "Prey-predator dynamics with prey refuge providing additional food to predator," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 110-119.
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    2. Ghanbari, Behzad & Günerhan, Hatıra & Srivastava, H.M., 2020. "An application of the Atangana-Baleanu fractional derivative in mathematical biology: A three-species predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Liu, He & Dai, Chuanjun & Yu, Hengguo & Guo, Qing & Li, Jianbing & Hao, Aimin & Kikuchi, Jun & Zhao, Min, 2023. "Dynamics of a stochastic non-autonomous phytoplankton–zooplankton system involving toxin-producing phytoplankton and impulsive perturbations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 368-386.

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