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Influence of environmental noises on a prey–predator species with predator-dependent carrying capacity in alpine meadow ecosystem

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  • Das, Amartya
  • Samanta, G.P.

Abstract

Degradation of carrying capacity due to any reason is a serious concern for ecosystem as well as for dynamical system. It is observed in alpine meadow ecosystem that carrying capacity of vegetation reduces due to digging holes, throwing out soils, piling up mounds by plateau pika. In this ecosystem, it is also observed that height of vegetation increases death rate of plateau pika. These two facts when considered with environmental fluctuation make it an interesting topic of discussion in dynamical system. This motivation leads us to a stochastic analysis of a prey–predator model in alpine meadow ecosystem. In this analysis, Gaussian White noise has been introduced to exhibit the influence of environmental fluctuations on prey’s growth rate and predator’s death rate. We have established positivity and boundedness of the system theoretically. Extinction scenario, persistence of the system and global attractivity of solutions are also established. Numerical simulation validates theoretical results. Moreover, the appropriateness of the model in numerical simulation has also been justified with the help of some field experimental data. In discussion section, another approach for formulating the model has also been discussed.

Suggested Citation

  • Das, Amartya & Samanta, G.P., 2021. "Influence of environmental noises on a prey–predator species with predator-dependent carrying capacity in alpine meadow ecosystem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1294-1316.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:1294-1316
    DOI: 10.1016/j.matcom.2021.07.014
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    References listed on IDEAS

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    1. Yong Ye & Hua Liu & Yu-mei Wei & Ming Ma & Kai Zhang, 2019. "Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-15, August.
    2. 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.
    3. G. P. Samanta, 2011. "A Stochastic Two Species Competition Model: Nonequilibrium Fluctuation and Stability," International Journal of Stochastic Analysis, Hindawi, vol. 2011, pages 1-7, April.
    4. Lu Wen & Shikui Dong & Yuanyuan Li & Xiaoyan Li & Jianjun Shi & Yanlong Wang & Demei Liu & Yushou Ma, 2013. "Effect of Degradation Intensity on Grassland Ecosystem Services in the Alpine Region of Qinghai-Tibetan Plateau, China," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-8, March.
    5. 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).
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