IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v177y2023ics0960077923011232.html
   My bibliography  Save this article

Dynamics of a diffusive predator–prey model with nonlocal fear effect

Author

Listed:
  • Sun, Xiuli

Abstract

The fear effect on prey populations due to the presence of a predator’s sound or smell can be more impactful than direct predation. In this paper, we formulate a diffusive predator–prey model incorporating the nonlocal fear effect. The existence and boundedness of solutions are showed. We also study the stability of constant steady states by using the characteristic equation and Lyapunov functionals. Steady-state bifurcations are carried out in detail by the Lyapunov-Schmidt method. The analyses demonstrate that the fear effect in the system can change the stability of the constant steady state and there exist spatially nonhomogeneous steady states. Hopf bifurcations are also investigated and the results show that high levels of fear can stabilize the model by excluding the existence of periodic solutions. Finally, numerical simulations are sketched to illustrate our theoretical findings. This work can help us further understand the impact of fear effect on the stability of constant steady states, steady-state bifurcations and Hopf bifurcations of predator–prey models.

Suggested Citation

  • Sun, Xiuli, 2023. "Dynamics of a diffusive predator–prey model with nonlocal fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011232
    DOI: 10.1016/j.chaos.2023.114221
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923011232
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114221?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Kaur, Rajinder Pal & Sharma, Amit & Sharma, Anuj Kumar, 2021. "Impact of fear effect on plankton-fish system dynamics incorporating zooplankton refuge," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
    3. Duan, Daifeng & Niu, Ben & Wei, Junjie, 2019. "Hopf-Hopf bifurcation and chaotic attractors in a delayed diffusive predator-prey model with fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 206-216.
    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. Du, Yanfei & Sui, Mengting, 2024. "Stability and spatiotemporal dynamics in a diffusive predator–prey model with nonlocal prey competition and nonlocal fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 188(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. 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).
    2. Rashi, & Singh, Harendra Pal & Singh, Suruchi, 2024. "Effect of fear with saturated fear cost and harvesting on aquatic food chain model (plankton–fish model) in the presence of nanoparticles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 283-305.
    3. Ma, Tingting & Meng, Xinzhu & Hayat, Tasawar & Hobiny, Aatef, 2021. "Stability analysis and optimal harvesting control of a cross-diffusion prey-predator system," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Chen, Mengxin & Zheng, Qianqian, 2023. "Steady state bifurcation of a population model with chemotaxis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    5. Zhang, Baoxiang & Cai, Yongli & Wang, Bingxian & Wang, Weiming, 2019. "Pattern formation in a reaction–diffusion parasite–host model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 732-740.
    6. 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).
    7. Xiaoran Wang & Huimei Liu & Wencai Zhao, 2024. "A Predator–Prey System with a Modified Leslie–Gower and Prey Stage Structure Scheme in Deterministic and Stochastic Environments," Mathematics, MDPI, vol. 12(15), pages 1-26, July.
    8. Barman, Dipesh & Roy, Jyotirmoy & Alrabaiah, Hussam & Panja, Prabir & Mondal, Sankar Prasad & Alam, Shariful, 2021. "Impact of predator incited fear and prey refuge in a fractional order prey predator model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    9. Debasis Mukherjee, 2025. "Dynamics of a Stochastic Predator-Prey System in Presence of Competitor for Prey with Fear Effect and Hunting Cooperation," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-15, June.
    10. Chen Zhang & Xianyi Li, 2023. "Dynamics of a Discrete Leslie–Gower Model with Harvesting and Holling-II Functional Response," Mathematics, MDPI, vol. 11(15), pages 1-19, July.
    11. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution of a stochastic cholera model between communities linked by migration," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    12. Saha, Sangeeta & Pal, Swadesh & Melnik, Roderick, 2025. "Analysis of the impact of fear in the presence of additional food and prey refuge with nonlocal predator–prey models," Ecological Modelling, Elsevier, vol. 505(C).
    13. Ai, Xin & Zhang, Yue, 2025. "Dynamic analysis of phytoplankton–zooplankton–fish singular perturbation system on three time-scales," Chaos, Solitons & Fractals, Elsevier, vol. 190(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. Kumbhakar, Ruma & Hossain, Mainul & Karmakar, Sarbari & Pal, Nikhil, 2024. "An investigation of the parameter space in a tri-trophic food chain model with refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 37-59.
    16. 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.
    17. Tang, Xiaosong, 2022. "Periodic solutions and spatial patterns induced by mixed delays in a diffusive spruce budworm model with Holling II predation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 420-429.
    18. Cheng, Haihui & Meng, Xinzhu & Hayat, Tasawar & Hobiny, Aatef, 2023. "Multistability and bifurcation analysis for a three-strategy game system with public goods feedback and discrete delays," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    19. Sajan, & Dubey, Balram & Sasmal, Sourav Kumar, 2022. "Chaotic dynamics of a plankton-fish system with fear and its carry over effects in the presence of a discrete delay," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    20. Kaur, Rajinder Pal & Sharma, Amit & Sharma, Anuj Kumar, 2021. "Impact of fear effect on plankton-fish system dynamics incorporating zooplankton refuge," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:177:y:2023:i:c:s0960077923011232. 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.