IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v170y2020icp366-378.html
   My bibliography  Save this article

Dynamics analysis of a predator–prey model with herd behavior and nonlocal prey competition

Author

Listed:
  • Peng, Yahong
  • Zhang, Guoying

Abstract

Nonlocal reaction–diffusion model is an important area to study the dynamics of the individuals which compete for resources. In this paper, we consider a predator–prey model with herd behavior and nonlocal prey competition. We investigate the effects of nonlocal competition on dynamics of the system in the bounded region when the kernel function takes 1|Ω| and derive the conditions that the nonlocal system undergoes Hopf bifurcation and Turing bifurcation. Then we discuss the influence of nonlocal competition on the stability of the positive constant equilibrium in unbounded region when the kernel function takes a step kernel function. Our result shows that nonlocal competition can destabilize the stability of the predator–prey system.

Suggested Citation

  • Peng, Yahong & Zhang, Guoying, 2020. "Dynamics analysis of a predator–prey model with herd behavior and nonlocal prey competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 366-378.
  • Handle: RePEc:eee:matcom:v:170:y:2020:i:c:p:366-378
    DOI: 10.1016/j.matcom.2019.11.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475419303453
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2019.11.012?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. Merchant, Sandra M. & Nagata, Wayne, 2011. "Instabilities and spatiotemporal patterns behind predator invasions with nonlocal prey competition," Theoretical Population Biology, Elsevier, vol. 80(4), pages 289-297.
    2. Peng, Yahong & Ling, Heyang, 2018. "Pattern formation in a ratio-dependent predator-prey model with cross-diffusion," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 307-318.
    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. Yang, Youwei & Wu, Daiyong & Shen, Chuansheng & Lu, Fengping, 2023. "Allee effect in a diffusive predator–prey system with nonlocal prey competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    2. Kumar, Sunil & Kumar, Ranbir & Cattani, Carlo & Samet, Bessem, 2020. "Chaotic behaviour of fractional predator-prey dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    3. Shi, Qingyan & Song, Yongli, 2022. "Spatiotemporal pattern formation in a pollen tube model with nonlocal effect and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    4. Du, Wentong & Xiao, Min & Ding, Jie & Yao, Yi & Wang, Zhengxin & Yang, Xinsong, 2023. "Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 414-438.

    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. Meng Zhu & Jing Li & Xinze Lian, 2022. "Pattern Dynamics of Cross Diffusion Predator–Prey System with Strong Allee Effect and Hunting Cooperation," Mathematics, MDPI, vol. 10(17), pages 1-20, September.
    2. Souna, Fethi & Belabbas, Mustapha & Menacer, Youssaf, 2023. "Complex pattern formations induced by the presence of cross-diffusion in a generalized predator–prey model incorporating the Holling type functional response and generalization of habitat complexity e," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 597-618.
    3. Yang, Feng & Song, Yongli, 2022. "Stability and spatiotemporal dynamics of a diffusive predator–prey system with generalist predator and nonlocal intraspecific competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 159-168.
    4. Yangyang Shao & Yan Meng & Xinyue Xu, 2022. "Turing Instability and Spatiotemporal Pattern Formation Induced by Nonlinear Reaction Cross-Diffusion in a Predator–Prey System with Allee Effect," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
    5. Sajan, & Anshu, & Dubey, Balram, 2024. "Study of a cannibalistic prey–predator model with Allee effect in prey under the presence of diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    6. Mohan, Nishith & Kumari, Nitu, 2021. "Positive steady states of a SI epidemic model with cross diffusion," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    7. Kalyan Manna & Vitaly Volpert & Malay Banerjee, 2020. "Dynamics of a Diffusive Two-Prey-One-Predator Model with Nonlocal Intra-Specific Competition for Both the Prey Species," Mathematics, MDPI, vol. 8(1), pages 1-28, January.
    8. Yang, Youwei & Wu, Daiyong & Shen, Chuansheng & Lu, Fengping, 2023. "Allee effect in a diffusive predator–prey system with nonlocal prey competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    9. Chakraborty, Bhaskar & Ghorai, Santu & Bairagi, Nandadulal, 2020. "Reaction-diffusion predator-prey-parasite system and spatiotemporal complexity," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    10. Wang, Henan & Liu, Ping, 2023. "Pattern dynamics of a predator–prey system with cross-diffusion, Allee effect and generalized Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 171(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:matcom:v:170:y:2020:i:c:p:366-378. 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/mathematics-and-computers-in-simulation/ .

    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.