IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i18p3270-d910389.html
   My bibliography  Save this article

Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour

Author

Listed:
  • Zhenglong Chen

    (School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

  • Shunjie Li

    (School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

  • Xuebing Zhang

    (School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

Abstract

This paper is devoted to studying the dynamics of a delayed reaction-diffusion predator–prey system incorporating the effects of fear and anti-predator behaviour. First, based on its mathematical model, the global attractor is analyzed and the local stability of its positive equilibria is derived. Moreover, the Hopf bifurcation induced by the time delay variable is also investigated. Furthermore, the existence and non-existence of non-constant positive solutions are analyzed. Finally, numerical simulations are presented to validate the theoretical analysis.

Suggested Citation

  • Zhenglong Chen & Shunjie Li & Xuebing Zhang, 2022. "Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour," Mathematics, MDPI, vol. 10(18), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3270-:d:910389
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/18/3270/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/18/3270/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yang, Ruizhi & Ma, Jian, 2018. "Analysis of a diffusive predator-prey system with anti-predator behaviour and maturation delay," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 128-139.
    2. Panday, Pijush & Samanta, Sudip & Pal, Nikhil & Chattopadhyay, Joydev, 2020. "Delay induced multiple stability switch and chaos in a predator–prey model with fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 134-158.
    3. 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.
    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. 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. 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.
    3. Li, Yajing & He, Mengxin & Li, Zhong, 2022. "Dynamics of a ratio-dependent Leslie–Gower predator–prey model with Allee effect and fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 417-439.
    4. 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.
    5. Zainab Saeed Abbas & Raid Kamel Naji, 2022. "Modeling and Analysis of the Influence of Fear on a Harvested Food Web System," Mathematics, MDPI, vol. 10(18), pages 1-37, September.
    6. 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.
    7. 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.
    8. Balcı, Ercan, 2023. "Predation fear and its carry-over effect in a fractional order prey–predator model with prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    9. 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.
    10. 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).
    11. Arjun Hasibuan & Asep Kuswandi Supriatna & Endang Rusyaman & Md. Haider Ali Biswas, 2023. "Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    12. Das, Amartya & Samanta, G.P., 2020. "A prey–predator model with refuge for prey and additional food for predator in a fluctuating environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    13. Wang, Jingjing & Zheng, Hongchan & Jia, Yunfeng, 2021. "Dynamical analysis on a bacteria-phages model with delay and diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    14. 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.
    15. 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.
    16. 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).
    17. Han, Bingtao & Jiang, Daqing, 2022. "Stationary distribution, extinction and density function of a stochastic prey-predator system with general anti-predator behavior and fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    18. Das, Bijoy Kumar & Sahoo, Debgopal & Samanta, G.P., 2022. "Impact of fear in a delay-induced predator–prey system with intraspecific competition within predator species," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 134-156.
    19. Tiancai Liao & Hengguo Yu & Chuanjun Dai & Min Zhao, 2019. "Impact of Cell Size Effect on Nutrient-Phytoplankton Dynamics," Complexity, Hindawi, vol. 2019, pages 1-23, November.
    20. 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.

    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:gam:jmathe:v:10:y:2022:i:18:p:3270-:d:910389. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.