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Survival analysis of a stochastic service–resource mutualism model in a polluted environment with pulse toxicant input

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  • Wang, Hui
  • Pan, Fangmei
  • Liu, Meng

Abstract

In this paper, taking the white noises, Markovian switching and Lévy jumps into account, a stochastic service–resource mutualism model in a polluted environment with pulse toxicant input is proposed and analyzed. The critical value between persistence in the mean and extinction for each species is obtained. Several numerical simulations are also introduced to illustrate the theoretical results. The results reveal that random perturbations, the impulsive period and the toxicant input amount each time have close relationships with the persistence and extinction of the species.

Suggested Citation

  • Wang, Hui & Pan, Fangmei & Liu, Meng, 2019. "Survival analysis of a stochastic service–resource mutualism model in a polluted environment with pulse toxicant input," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 591-606.
    • Handle: RePEc:eee:phsmap:v:521:y:2019:i:c:p:591-606
    DOI: 10.1016/j.physa.2019.01.108
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    References listed on IDEAS

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    1. Yang, Xiaofeng & Jin, Zhen & Xue, Yakui, 2007. "Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 726-735.
    2. Wu, Jian, 2018. "Stability of a three-species stochastic delay predator–prey system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 492-505.
    3. Zhao, Yu & Yuan, Sanling, 2017. "Optimal harvesting policy of a stochastic two-species competitive model with Lévy noise in a polluted environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 20-33.
    4. Zhang, Xinhong & Jiang, Daqing & Alsaedi, Ahmed & Hayat, Tasawar, 2016. "Periodic solutions and stationary distribution of mutualism models in random environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 270-282.
    5. Liu, Meng & Yu, Jingyi & Mandal, Partha Sarathi, 2018. "Dynamics of a stochastic delay competitive model with harvesting and Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 335-349.
    6. Kunita, Hiroshi, 2010. "Itô's stochastic calculus: Its surprising power for applications," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 622-652, May.
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