IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i13p2262-d850256.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/13/2262/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/13/2262/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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).
    2. 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).
    3. 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).
    4. 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).
    5. 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.
    6. 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).
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Saha, Pritam & Mondal, Bapin & Ghosh, Uttam, 2023. "Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Sabbar, Yassine & Din, Anwarud & Kiouach, Driss, 2023. "Influence of fractal–fractional differentiation and independent quadratic Lévy jumps on the dynamics of a general epidemic model with vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    4. Din, Anwarud & Li, Yongjin & Yusuf, Abdullahi, 2021. "Delayed hepatitis B epidemic model with stochastic analysis," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Xuan Leng & Asad Khan & Anwarud Din, 2023. "Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    6. Zai-Yin He & Abderrahmane Abbes & Hadi Jahanshahi & Naif D. Alotaibi & Ye Wang, 2022. "Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
    7. Nikolaos P. Rachaniotis & Thomas K. Dasaklis & Filippos Fotopoulos & Platon Tinios, 2021. "A Two-Phase Stochastic Dynamic Model for COVID-19 Mid-Term Policy Recommendations in Greece: A Pathway towards Mass Vaccination," IJERPH, MDPI, vol. 18(5), pages 1-21, March.
    8. Yassine Sabbar & Mohammad Izadi & Aeshah A. Raezah & Waleed Adel, 2024. "Nonlinear Dynamics of a General Stochastic SIR Model with Behavioral and Physical Changes: Analysis and Application to Zoonotic Tuberculosis," Mathematics, MDPI, vol. 12(13), pages 1-17, June.
    9. Liao, Tiancai, 2024. "The impact of temperature variation on the algae–zooplankton dynamics with size-selective disturbance," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    10. Ihtisham Ul Haq & Numan Ullah & Nigar Ali & Kottakkaran Sooppy Nisar, 2022. "A New Mathematical Model of COVID-19 with Quarantine and Vaccination," Mathematics, MDPI, vol. 11(1), pages 1-21, December.
    11. Marsa Gholamzadeh & Hamidreza Abtahi & Reza Safdari, 2021. "Suggesting a framework for preparedness against the pandemic outbreak based on medical informatics solutions: a thematic analysis," International Journal of Health Planning and Management, Wiley Blackwell, vol. 36(3), pages 754-783, May.
    12. Yuanlin Ma & Xingwang Yu, 2022. "Stationary Probability Density Analysis for the Randomly Forced Phytoplankton–Zooplankton Model with Correlated Colored Noises," Mathematics, MDPI, vol. 10(14), pages 1-11, July.
    13. Singh, Harendra, 2021. "Analysis of drug treatment of the fractional HIV infection model of CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    14. Elaiw, A.M. & Alsaedi, A.J. & Hobiny, A.D. & Aly, S., 2023. "Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    15. Babaei, A. & Jafari, H. & Banihashemi, S. & Ahmadi, M., 2021. "Mathematical analysis of a stochastic model for spread of Coronavirus," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    16. Yu, Zhenhua & Arif, Robia & Fahmy, Mohamed Abdelsabour & Sohail, Ayesha, 2021. "Self organizing maps for the parametric analysis of COVID-19 SEIRS delayed model," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    17. Zhang, Zhenzhong & Zhang, Xuekang & Tong, Jinying, 2017. "Exponential ergodicity for population dynamics driven by α-stable processes," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 149-159.
    18. ur Rahman, Ghaus & Badshah, Qaisar & Agarwal, Ravi P. & Islam, Saeed, 2021. "Ergodicity & dynamical aspects of a stochastic childhood disease model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 738-764.
    19. Yehuda Arav & Eyal Fattal & Ziv Klausner, 2022. "Is the Increased Transmissibility of SARS-CoV-2 Variants Driven by within or Outside-Host Processes?," Mathematics, MDPI, vol. 10(19), pages 1-17, September.
    20. Hussain, Takasar & Aslam, Adnan & Ozair, Muhammad & Tasneem, Fatima & Gómez-Aguilar, J.F., 2021. "Dynamical aspects of pine wilt disease and control measures," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2262-:d:850256. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.