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Probabilistic Analysis of a Marine Ecological System with Intense Variability

Author

Listed:
  • Yassine Sabbar

    (LPAIS Laboratory, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez 30000, Morocco)

  • Asad Khan

    (School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China)

  • Anwarud Din

    (Department of Mathematics, Sun Yat-sen University, Guangzhou 510006, China)

Abstract

This work seeks to simulate and examine the complex character of marine predation. By taking into account the interaction between phytoplankton and zooplankton , we present a sophisticated mathematical system with a general functional response describing the ecological competition. This system is disturbed by a novel category of perturbations in the hybrid form which simulates certain unstable climatic and environmental variations. We merge between the higher-order white noise and quadratic jumps to offer an excellent overview of the complexity induced in the ecosystem. Analytically, we offer a surrogate framework to get the sharp sill between stationarity and zooplankton eradication. Our analysis enriches and improves many works by proposing an unfamiliar form of perturbation and unifying the criteria of said asymptotic characteristics. Numerically, we probe the rigor of our sill in a non-standard case: cubic white noise and quadratic leaps. We demonstrate that the increased order of perturbation has a significant effect on the zooplankton living time. This result shows that the sources of intricate fluctuations carry out an active role in the transient dynamics of marine ecological systems.

Suggested Citation

  • Yassine Sabbar & Asad Khan & Anwarud Din, 2022. "Probabilistic Analysis of a Marine Ecological System with Intense Variability," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2262-:d:850256
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    References listed on IDEAS

    as
    1. Din, Anwarud & Li, Yongjin & Khan, Tahir & Zaman, Gul, 2020. "Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Din, Anwarud & Khan, Amir & Baleanu, Dumitru, 2020. "Stationary distribution and extinction of stochastic coronavirus (COVID-19) epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Tong, Jinying & Zhang, Zhenzhong & Bao, Jianhai, 2013. "The stationary distribution of the facultative population model with a degenerate noise," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 655-664.
    4. Liao, Tiancai, 2022. "The impact of plankton body size on phytoplankton-zooplankton dynamics in the absence and presence of stochastic environmental fluctuation," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    5. Hussain, Ghulam & Khan, Amir & Zahri, Mostafa & Zaman, Gul, 2020. "Stochastic permanence of an epidemic model with a saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Sabbar, Yassine & Kiouach, Driss & Rajasekar, S.P. & El-idrissi, Salim El Azami, 2022. "The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: New framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    7. Driss Kiouach & Yassine Sabbar, 2018. "Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible Individuals," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-13, May.
    8. Zhao, Dianli & Yuan, Sanling, 2018. "Sharp conditions for the existence of a stationary distribution in one classical stochastic chemostat," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 199-205.
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