IDEAS home Printed from https://ideas.repec.org/a/spr/endesu/v23y2021i6d10.1007_s10668-020-01024-1.html
   My bibliography  Save this article

Impact of adult predator incited fear in a stage-structured prey–predator model

Author

Listed:
  • Narayan Mondal

    (Indian Institute of Engineering Science and Technology, Shibpur)

  • Dipesh Barman

    (Indian Institute of Engineering Science and Technology, Shibpur)

  • Shariful Alam

    (Indian Institute of Engineering Science and Technology, Shibpur)

Abstract

A two-species predator–prey model where the predators are separated into juvenile and mature predators has been considered in this article. Here, functional response in linear form is considered to know the impact of adult predator-induced fear in the stage-structured prey–predator model. Positivity and boundedness of the model system have been checked. Persistence conditions and existence condition(s) of each equilibria have been derived. The local and global stability analysis have been implemented both analytically and numerically along with Hopf bifurcation analysis with direction. From the analysis of the model system, it is observed that the mature predator-induced fear and rate of transition from juvenile (minor) predator to mature predator plays a crucial role in controlling the system dynamics.

Suggested Citation

  • Narayan Mondal & Dipesh Barman & Shariful Alam, 2021. "Impact of adult predator incited fear in a stage-structured prey–predator model," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(6), pages 9280-9307, June.
    • Handle: RePEc:spr:endesu:v:23:y:2021:i:6:d:10.1007_s10668-020-01024-1
    DOI: 10.1007/s10668-020-01024-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10668-020-01024-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10668-020-01024-1?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. Meng, Xin-You & Huo, Hai-Feng & Xiang, Hong & Yin, Qi-yu, 2014. "Stability in a predator–prey model with Crowley–Martin function and stage structure for prey," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 810-819.
    2. Kundu, Soumen & Maitra, Sarit, 2018. "Dynamics of a delayed predator-prey system with stage structure and cooperation for preys," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 453-460.
    3. Lu, Yang & Pawelek, Kasia A. & Liu, Shengqiang, 2017. "A stage-structured predator-prey model with predation over juvenile prey," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 115-130.
    4. Evan L Preisser & Daniel I Bolnick, 2008. "The Many Faces of Fear: Comparing the Pathways and Impacts of Nonconsumptive Predator Effects on Prey Populations," PLOS ONE, Public Library of Science, vol. 3(6), pages 1-8, June.
    5. Khajanchi, Subhas, 2017. "Modeling the dynamics of stage-structure predator-prey system with Monod–Haldane type response function," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 122-143.
    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. Dubey, Balram & Sajan, & Kumar, Ankit, 2021. "Stability switching and chaos in a multiple delayed prey–predator model with fear effect and anti-predator behavior," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 164-192.
    2. Jaouad Danane & Delfim F. M. Torres, 2023. "Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species," Mathematics, MDPI, vol. 11(7), pages 1-22, March.
    3. Ma, Yuanyuan & Dong, Nan & Liu, Na & Xie, Leilei, 2022. "Spatiotemporal and bifurcation characteristics of a nonlinear prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    4. 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).
    5. Liu, Junli & Liu, Bairu & Lv, Pan & Zhang, Tailei, 2021. "An eco-epidemiological model with fear effect and hunting cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    6. Thirthar, Ashraf Adnan & Majeed, Salam J. & Alqudah, Manar A. & Panja, Prabir & Abdeljawad, Thabet, 2022. "Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    7. Tiwari, Vandana & Tripathi, Jai Prakash & Mishra, Swati & Upadhyay, Ranjit Kumar, 2020. "Modeling the fear effect and stability of non-equilibrium patterns in mutually interfering predator–prey systems," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    8. Maiti, Atasi Patra & Dubey, B. & Chakraborty, A., 2019. "Global analysis of a delayed stage structure prey–predator model with Crowley–Martin type functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 58-84.
    9. Yangyang Su & Tongqian Zhang, 2022. "Global Dynamics of a Predator–Prey Model with Fear Effect and Impulsive State Feedback Control," Mathematics, MDPI, vol. 10(8), pages 1-23, April.
    10. Seralan Vinoth & R. Vadivel & Nien-Tsu Hu & Chin-Sheng Chen & Nallappan Gunasekaran, 2023. "Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge," Mathematics, MDPI, vol. 11(14), pages 1-25, July.
    11. Khajanchi, Subhas, 2021. "The impact of immunotherapy on a glioma immune interaction model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    12. Sardar, Mrinmoy & Biswas, Santosh & Khajanchi, Subhas, 2021. "The impact of distributed time delay in a tumor-immune interaction system," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    13. Zhang, Shengqiang & Yuan, Sanling & Zhang, Tonghua, 2022. "A predator-prey model with different response functions to juvenile and adult prey in deterministic and stochastic environments," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    14. 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.
    15. Mukherjee, Debasis, 2020. "Role of fear in predator–prey system with intraspecific competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 263-275.
    16. Zhao, Xin & Zeng, Zhijun, 2020. "Stationary distribution of a stochastic predator–prey system with stage structure for prey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    17. Liu, Yujuan & Lu, Qiong, 2020. "Hopf bifurcations in 3D competitive system with mixing exponential and rational growth rates," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    18. Sahu, S.R. & Raw, S.N., 2023. "Appearance of chaos and bi-stability in a fear induced delayed predator–prey system: A mathematical modeling study," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    19. Mingjing Du & Junmei Li & Yulan Wang & Wei Zhang, 2019. "Numerical Simulation of a Class of Three-Dimensional Kolmogorov Model with Chaotic Dynamic Behavior by Using Barycentric Interpolation Collocation Method," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    20. Yousef, Fatma Bozkurt & Yousef, Ali & Maji, Chandan, 2021. "Effects of fear in a fractional-order predator-prey system with predator density-dependent prey mortality," 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:spr:endesu:v:23:y:2021:i:6:d:10.1007_s10668-020-01024-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.