IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v611y2023ics0378437123000249.html
   My bibliography  Save this article

A study of Michaelis–Menten type harvesting effects on a population in stochastic environment

Author

Listed:
  • Mandal, Saroj Kumar
  • Poria, Swarup

Abstract

In this paper, a study of Michaelis–Menten type harvesting effects on a population with outbreak characteristic in stochastic environment is done formulating stochastic model. The Ludwig model (Ludwig et al., 1978) is chosen as the base mathematical model for the population. Steady state probability distribution and stationary potential function of the population are determined. P-bifurcation analysis has been presented. The impact of the noises and cross correlations strength on outbreak and extinction of the population are measured numerically using probability. It is observed that random rate of Michaelis–Menten type harvesting may extinct the population. The choice of noise or type of harvesting process to population control cannot be uniquely defined and deeply depends on the exogenous factors (extrinsic and intrinsic noise), a contradiction to the earlier reports. Various complex ecological phenomena like noise enhance stability, phase regime shift, etc., are identified in the system.

Suggested Citation

  • Mandal, Saroj Kumar & Poria, Swarup, 2023. "A study of Michaelis–Menten type harvesting effects on a population in stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    • Handle: RePEc:eee:phsmap:v:611:y:2023:i:c:s0378437123000249
    DOI: 10.1016/j.physa.2023.128469
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123000249
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2023.128469?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. Zeng, Chunhua & Zeng, Chunping & Gong, Ailing & Nie, Linru, 2010. "Effect of time delay in FitzHugh–Nagumo neural model with correlations between multiplicative and additive noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5117-5127.
    3. Han, Ping & Xu, Wei & Wang, Liang & Zhang, Hongxia & Ma, Shichao, 2020. "Most probable dynamics of the tumor growth model with immune surveillance under cross-correlated noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    4. Guttal, Vishwesha & Jayaprakash, C., 2007. "Impact of noise on bistable ecological systems," Ecological Modelling, Elsevier, vol. 201(3), pages 420-428.
    5. Liu, Jian & Cao, Jie & Wang, Youguo & Hu, Bing, 2019. "Asymmetric stochastic resonance in a bistable system driven by non-Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 321-336.
    6. Han, Qinglin & Yang, Tao & Zeng, Chunhua & Wang, Hua & Liu, Zhiqiang & Fu, Yunchang & Zhang, Chun & Tian, Dong, 2014. "Impact of time delays on stochastic resonance in an ecological system describing vegetation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 96-105.
    7. Das, Parthasakha & Mukherjee, Sayan & Das, Pritha, 2019. "An investigation on Michaelis - Menten kinetics based complex dynamics of tumor - immune interaction," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 297-305.
    8. Das, Parthasakha & Das, Pritha & Mukherjee, Sayan, 2020. "Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    9. Du, Lu-Chun & Mei, Dong-Cheng, 2011. "Stochastic resonance, reverse-resonance and stochastic multi-resonance in an underdamped quartic double-well potential with noise and delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3262-3266.
    10. Jin, Yanfei, 2012. "Noise-induced dynamics in a delayed bistable system with correlated noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 1928-1933.
    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. Zeng, Chunhua & Wang, Hua, 2012. "Noise and large time delay: Accelerated catastrophic regime shifts in ecosystems," Ecological Modelling, Elsevier, vol. 233(C), pages 52-58.
    2. Zhao, Zhong & Pang, Liuyong & Li, Qiuying, 2021. "Analysis of a hybrid impulsive tumor-immune model with immunotherapy and chemotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Shi, Peiming & Xia, Haifeng & Han, Dongying & Fu, Rongrong & Yuan, Danzhen, 2018. "Stochastic resonance in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 8-14.
    4. Das, Parthasakha & Das, Samhita & Das, Pritha & Rihan, Fathalla A. & Uzuntarla, Muhammet & Ghosh, Dibakar, 2021. "Optimal control strategy for cancer remission using combinatorial therapy: A mathematical model-based approach," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Zhang, Hongxia & Xu, Wei & Han, Ping & Qiao, Yan, 2020. "Stochastic dynamic balance of a bi-stable vegetation model with pulse control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    6. Liu, Jian & Qiao, Zijian & Ding, Xiaojian & Hu, Bing & Zang, Chuanlai, 2021. "Stochastic resonance induced weak signal enhancement over controllable potential-well asymmetry," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. Gong, Xulu & Xu, Pengfei & Liu, Di & Zhou, Biliu, 2023. "Stochastic resonance of multi-stable energy harvesting system with high-order stiffness from rotational environment," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    8. Yang, Yafei & Fan, Meng, 2023. "Impact of selective grazing on the dynamics of a diffusive plankton model with component Allee effect and additional food," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    9. Wang, Min & Fang, Yuwen & Luo, Yuhui & Yang, Fengzao & Zeng, Chunhua & Duan, Wei-Long, 2019. "Influence of non-Gaussian noise on the coherent feed-forward loop with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 46-55.
    10. Meng, Qingyan & Wang, Yejuan & Kloeden, Peter E., 2023. "The dynamical behavior of a class of stochastic vegetation models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 341-367.
    11. Das, Parthasakha & Das, Pritha & Mukherjee, Sayan, 2020. "Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    12. Hao, Mengli & Jia, Wantao & Wang, Liang & Li, Fuxiao, 2022. "Most probable trajectory of a tumor model with immune response subjected to asymmetric Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    13. Li, Wei & Zhang, Ying & Huang, Dongmei & Rajic, Vesna, 2022. "Study on stationary probability density of a stochastic tumor-immune model with simulation by ANN algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    14. 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).
    15. Dong, Yang & Wen, Shu-hui & Hu, Xiao-bing & Li, Jiang-Cheng, 2020. "Stochastic resonance of drawdown risk in energy market prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    16. Xu, Pengfei & Jin, Yanfei, 2018. "Mean first-passage time in a delayed tristable system driven by correlated multiplicative and additive white noises," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 75-82.
    17. Othman Abdullah Almatroud & Amel Hioual & Adel Ouannas & Giuseppe Grassi, 2023. "On Fractional-Order Discrete-Time Reaction Diffusion Systems," Mathematics, MDPI, vol. 11(11), pages 1-16, May.
    18. Xu, Pengfei & Jin, Yanfei, 2020. "Coherence and stochastic resonance in a second-order asymmetric tri-stable system with memory effects," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    19. Bian, Junhao & Ma, Zhiqin & Wang, Chunping & Huang, Tao & Zeng, Chunhua, 2024. "Early warning for spatial ecological system: Fractal dimension and deep learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    20. Zeng, Yujie & Liu, Dedi & Guo, Shenglian & Xiong, Lihua & Liu, Pan & Chen, Jie & Yin, Jiabo & Wu, Zhenhui & Zhou, Wan, 2023. "Assessing the effects of water resources allocation on the uncertainty propagation in the water–energy–food–society (WEFS) nexus," Agricultural Water Management, Elsevier, vol. 282(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:eee:phsmap:v:611:y:2023:i:c:s0378437123000249. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.