IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v100y2017icp74-90.html
   My bibliography  Save this article

Complex behavior of prey-predator system exhibiting group defense: A mathematical modeling study

Author

Listed:
  • Raw, S.N.
  • Mishra, P.
  • Kumar, R.
  • Thakur, S.

Abstract

Defense mechanisms are very important to all animal life. Predators in every biome must eat to survive. With predators being top on the food chain and always on the lookout for a meal, prey must constantly avoid being eaten. In this paper, we have proposed and analyzed a tri-trophic predator–prey model of one prey and two predator exhibiting group defense mechanism. We have assumed Monod-Haldane functional response for interaction between species due to group defense ability of prey and middle predator. We have performed Kolmogorov and Hopf bifurcation analysis for the model system. Linear and global stability of the model system have been analyzed. Lyapunov exponents are computed numerically and 2D scan for different parameters of the model have performed to characterize the complex behavior of the model system. The numerical simulations shows the chaotic and periodic oscillations of the model system for certain range of parameter. We have drawn bifurcation diagrams for different parameter values which shows the complex dynamical behavior of model system. This work is an attempt to study the effect of group defense mechanism of prey in predator population and effect of immigration within top predator population is investigated. It is also observed that in the presence of group defense, the model system stabilizes after adding a small amount of constant immigration within top predator population.

Suggested Citation

  • Raw, S.N. & Mishra, P. & Kumar, R. & Thakur, S., 2017. "Complex behavior of prey-predator system exhibiting group defense: A mathematical modeling study," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 74-90.
  • Handle: RePEc:eee:chsofr:v:100:y:2017:i:c:p:74-90
    DOI: 10.1016/j.chaos.2017.05.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917301911
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2017.05.010?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. Liu, Zhijun & Tan, Ronghua, 2007. "Impulsive harvesting and stocking in a Monod–Haldane functional response predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 454-464.
    2. Naji, R.K. & Balasim, A.T., 2007. "On the dynamical behavior of three species food web model," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1636-1648.
    3. Naji, Raid Kamel & Balasim, Alla Tariq, 2007. "Dynamical behavior of a three species food chain model with Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1853-1866.
    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. Xiao Dai & Jian Wu & Liang Yan, 2018. "A Spatial Evolutionary Study of Technological Innovation Talents’ Sticky Wages and Technological Innovation Efficiency Based on the Perspective of Sustainable Development," Sustainability, MDPI, vol. 10(11), pages 1-19, November.
    2. Kumar, Sachin & Kharbanda, Harsha, 2019. "Chaotic behavior of predator-prey model with group defense and non-linear harvesting in prey," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 19-28.
    3. Qin, Wenjie & Tan, Xuewen & Tosato, Marco & Liu, Xinzhi, 2019. "Threshold control strategy for a non-smooth Filippov ecosystem with group defense," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    4. Attia, Nourhane & Akgül, Ali & Seba, Djamila & Nour, Abdelkader, 2020. "An efficient numerical technique for a biological population model of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. Mishra, P. & Raw, S.N. & Tiwari, B., 2019. "Study of a Leslie–Gower predator-prey model with prey defense and mutual interference of predators," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 1-16.
    6. Kumar, Vikas & Kumari, Nitu, 2021. "Bifurcation study and pattern formation analysis of a tritrophic food chain model with group defense and Ivlev-like nonmonotonic functional response," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    7. Alidousti, Javad & Ghafari, Elham, 2020. "Dynamic behavior of a fractional order prey-predator model with group defense," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).

    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. Zhao, Min & Lv, Songjuan, 2009. "Chaos in a three-species food chain model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2305-2316.
    2. Florencia Carusela, M. & Momo, Fernando R. & Romanelli, Lilia, 2009. "Competition, predation and coexistence in a three trophic system," Ecological Modelling, Elsevier, vol. 220(19), pages 2349-2352.
    3. Cai, Liming & Li, Xuezhi & Yu, Jingyuan & Zhu, Guangtian, 2009. "Dynamics of a nonautonomous predator–prey dispersion–delay system with Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2064-2075.
    4. Kaviya, R. & Priyanka, M. & Muthukumar, P., 2022. "Mean-square exponential stability of impulsive conformable fractional stochastic differential system with application on epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    5. Gupta, R.P. & Yadav, Dinesh K., 2023. "Nonlinear dynamics of a stage-structured interacting population model with honest signals and cues," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Xingjie Wu & Wei Du & Genan Pan & Wentao Huang, 2013. "The dynamical behaviors of a Ivlev-type two-prey two-predator system with impulsive effect," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(1), pages 1-27, February.
    7. Alidousti, Javad & Ghafari, Elham, 2020. "Dynamic behavior of a fractional order prey-predator model with group defense," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    8. Ivanov, Tihomir & Dimitrova, Neli, 2017. "A predator–prey model with generic birth and death rates for the predator and Beddington–DeAngelis functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 111-123.
    9. Jiao, Jianjun & Meng, Xinzhu & Chen, Lansun, 2009. "Harvesting policy for a delayed stage-structured Holling II predator–prey model with impulsive stocking prey," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 103-112.
    10. Chen, Yiping & Liu, Zhijun, 2009. "Modelling and analysis of an impulsive SI model with Monod-Haldane functional response," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1698-1714.
    11. Hiba Abdullah Ibrahim & Raid Kamel Naji, 2023. "The Impact of Fear on a Harvested Prey–Predator System with Disease in a Prey," Mathematics, MDPI, vol. 11(13), pages 1-28, June.
    12. Upadhyay, Ranjit Kumar & Naji, Raid Kamel, 2009. "Dynamics of a three species food chain model with Crowley–Martin type functional response," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1337-1346.
    13. Jiao, Jianjun & Chen, Lansun & Cai, Shaohong, 2009. "A delayed stage-structured Holling II predator–prey model with mutual interference and impulsive perturbations on predator," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1946-1955.
    14. Singh, Anuraj & Gakkhar, Sunita, 2015. "Controlling chaos in a food chain model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 115(C), pages 24-36.
    15. Srinivas, M.N. & Sreerag, C. & Madhusudanan, V. & Gul, Nadia & Khan, Zareen A. & Zeb, Anwar, 2022. "Spatial deployment and performance of diffusion coefficients of two preys and one predator ecological system," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

    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:chsofr:v:100:y:2017:i:c:p:74-90. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.