IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v534y2019ics0378437119313317.html
   My bibliography  Save this article

Dynamics of an additional food provided predator–prey system with prey refuge dependent on both species and constant harvest in predator

Author

Listed:
  • Mondal, Sudeshna
  • Samanta, G.P.

Abstract

In the present work, we investigate on the dynamics of predator–prey model with prey refuge in proportion to both species and the effect of additional food provided to the predator. A Holling type II functional response in presence of additional food is taken to represent the interaction between prey and predator. Positivity and uniform boundedness of the solutions of the system are discussed analytically. Existence of equilibrium points and their stability criteria are analysed. Condition for occurrence of Hopf-bifurcation is derived analytically. It is found that the consumption rate of predator plays an important role in the dynamics of present system. Also, discrete time lag (gestation delay) in the proposed model is incorporated to observe the switching behaviour of the delay parameter through Hopf-bifurcation. Moreover, this work aims to analyse the dynamical behaviour of the considered predator–prey model when the predator is harvested at a constant rate. Numerical simulations are performed to verify all the analytical results using MATLAB and MATCONT.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:534:y:2019:i:c:s0378437119313317
    DOI: 10.1016/j.physa.2019.122301
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119313317
    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.2019.122301?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. Sen, Moitri & Srinivasu, P.D.N. & Banerjee, Malay, 2015. "Global dynamics of an additional food provided predator–prey system with constant harvest in predators," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 193-211.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. 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).
    3. 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).
    4. Das, Meghadri & Samanta, G.P., 2020. "A delayed fractional order food chain model with fear effect and prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 218-245.
    5. Mondal, Sudeshna & Samanta, Guruprasad, 2022. "Dynamics of a delayed toxin producing plankton model with variable search rate of zooplankton," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 166-191.

    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. 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.
    2. Liu, Qun & Jiang, Daqing, 2023. "Analysis of a stochastic inshore–offshore hairtail fishery model with Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. Roy, Jyotirmoy & Alam, Shariful, 2020. "Fear factor in a prey–predator system in deterministic and stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    4. 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).
    5. Carlos Ramirez-Carrasco & Fernando Córdova-Lepe & Nelson Velásquez, 2022. "A Simple Stability Analysis for a Mathematical Model of Migration Due to Noise and Resources," Mathematics, MDPI, vol. 10(19), pages 1-10, September.
    6. Liu, Chao & Xun, Xinying & Zhang, Guilai & Li, Yuanke, 2020. "Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    7. Zhang, Qiumei & Jiang, Daqing, 2021. "Dynamics of stochastic predator-prey systems with continuous time delay," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Huda Abdul Satar & Raid Kamel Naji, 2019. "Stability and Bifurcation of a Prey-Predator-Scavenger Model in the Existence of Toxicant and Harvesting," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-17, March.
    9. Mondal, Bapin & Ghosh, Uttam & Rahman, Md Sadikur & Saha, Pritam & Sarkar, Susmita, 2022. "Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 111-135.
    10. Saikia, Munmi & Maiti, Atasi Patra & Devi, Anuradha, 2020. "Effect of habitat complexity on rhinoceros and tiger population model with additional food and poaching in Kaziranga National Park, Assam," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 169-191.

    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:534:y:2019:i:c:s0378437119313317. 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.