IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v119y2019icp19-28.html
   My bibliography  Save this article

Chaotic behavior of predator-prey model with group defense and non-linear harvesting in prey

Author

Listed:
  • Kumar, Sachin
  • Kharbanda, Harsha

Abstract

We discuss the stability and bifurcation analysis of predator-prey model in the presence of group defense and non-linear harvesting in prey. Mathematically, we analyze the dynamics of the system such as boundedness of the solutions, existence and stability conditions of the equilibrium points. The model undergoes saddle-node, transcritical and Hopf-Andronov bifurcations. The direction of Hopf bifurcation by calculating the first Lyapunov number is examined. The effects of prey harvesting rate and death rate of predator on the model by considering them as bifurcation parameters are analyzed. In this paper, we dedicate ourselves to the investigation of the complex dynamics of the model to maintain the coexistence of the species which is important for ecological balance in the real environment. Several numerical simulations are performed to substantiate our analytical findings.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:119:y:2019:i:c:p:19-28
    DOI: 10.1016/j.chaos.2018.12.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918303795
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.12.011?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. Bulai, Iulia Martina & Venturino, Ezio, 2017. "Shape effects on herd behavior in ecological interacting population models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 40-55.
    2. Zhang, Lei & Wang, Wenjuan & Xue, Yakui, 2009. "Spatiotemporal complexity of a predator–prey system with constant harvest rate," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 38-46.
    3. Salman, S.M. & Yousef, A.M. & Elsadany, A.A., 2016. "Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 20-31.
    4. 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.
    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. Kim, Sangkwon & Park, Jintae & Lee, Chaeyoung & Jeong, Darae & Choi, Yongho & Kwak, Soobin & Kim, Junseok, 2020. "Periodic travelling wave solutions for a reaction-diffusion system on landscape fitted domains," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Bentout, Soufiane & Djilali, Salih & Kumar, Sunil, 2021. "Mathematical analysis of the influence of prey escaping from prey herd on three species fractional predator-prey interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    3. Sahoo, Debgopal & Samanta, Guruprasad, 2023. "Modeling cooperative evolution in prey species using the snowdrift game with evolutionary impact on prey–predator dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    4. Umar Sharif, Umi Syahirah Binti & Mohd, Mohd Hafiz, 2022. "Combined influences of environmental enrichment and harvesting mediate rich dynamics in an intraguild predation fishery system," Ecological Modelling, Elsevier, vol. 474(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. Mortuja, Md Golam & Chaube, Mithilesh Kumar & Kumar, Santosh, 2021. "Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. 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.
    3. 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).
    4. Zhang, Limin & Zhang, Chaofeng & He, Zhirong, 2019. "Codimension-one and codimension-two bifurcations of a discrete predator–prey system with strong Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 155-178.
    5. Acotto, Francesca & Venturino, Ezio & Viscardi, Alberto, 2024. "Does a marginal contact with a native species living in a complex domain with a fractional dimension boundary represent a sufficient invasive mechanism for the establishment of a migrating population?," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    6. Alidousti, Javad & Ghafari, Elham, 2020. "Dynamic behavior of a fractional order prey-predator model with group defense," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    7. Zhang, Xue & Zhang, Qing-Ling & Liu, Chao & Xiang, Zhong-Yi, 2009. "Bifurcations of a singular prey–predator economic model with time delay and stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1485-1494.
    8. Souna, Fethi & Lakmeche, Abdelkader & Djilali, Salih, 2020. "Spatiotemporal patterns in a diffusive predator-prey model with protection zone and predator harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. Cecilia Berardo & Iulia Martina Bulai & Ezio Venturino, 2021. "Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators," Mathematics, MDPI, vol. 9(20), pages 1-18, October.
    10. Wang, Yong & Zhou, Xu & Jiang, Weihua, 2023. "Bifurcations in a diffusive predator–prey system with linear harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    11. Ezio Venturino, 2022. "Disease Spread among Hunted and Retaliating Herding Prey," Mathematics, MDPI, vol. 10(23), pages 1-21, November.
    12. Fu, Shuaiming & Luo, Jianfeng & Zhao, Yi, 2022. "Stability and bifurcations analysis in an ecoepidemic system with prey group defense and two infectious routes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 665-690.
    13. Jialin Chen & Xiaqing He & Fengde Chen, 2021. "The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    14. Castillo-Alvino, Hamlet Humberto & Marvá, Marcos, 2022. "Group defense promotes coexistence in interference competition: The Holling type IV competitive response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 426-445.
    15. Rajni, & Ghosh, Bapan, 2022. "Multistability, chaos and mean population density in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    16. 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).
    17. Uddin, Md. Jasim & Rana, Sarker Md. Sohel & Işık, Seval & Kangalgil, Figen, 2023. "On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    18. Ghorai, Santu & Poria, Swarup, 2016. "Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 57-67.
    19. 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.
    20. Gupta, Ashvini & Dubey, Balram, 2022. "Bifurcation and chaos in a delayed eco-epidemic model induced by prey configuration," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

    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:119:y:2019:i:c:p:19-28. 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.