IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v143y2021ics0960077920309541.html
   My bibliography  Save this article

Impact of fear effect on plankton-fish system dynamics incorporating zooplankton refuge

Author

Listed:
  • Kaur, Rajinder Pal
  • Sharma, Amit
  • Sharma, Anuj Kumar

Abstract

In this paper, we analyze the impact of anti-predator behavior due to fear effect (K) and zooplankton refuge (r1) on a 3-D plankton-fish dynamical system involving phytoplankton, zooplankton, and fish species. We assume that zooplankton species have developed defense mechanisms against fish predation. The fear of fish predation altered anti-predator defenses, which affects the growth of the fish population. On the other hand, zooplankton refuge reduces fish induced mortality of zooplankton and plays a significant role in controlling phytoplankton growth. The density of fish species is suppressed in the presence of high refuge and the anti-predator response of zooplankton. It is determined that K and r1 can influence not only plankton-fish demography but also induce some mechanism to terminate planktonic blooms. Our mathematical study reveals that the low level of fear can stabilize the system dynamics in the presence of high rate of zooplankton refuge. Moreover, the low rate of zooplankton refuge can exclude complexity from the plankton-fish ecosystem in the presence of strong anti-predator responses of zooplankton. We have established the existence of all feasible biological equilibria and derived the conditional local and global stability of the given system around it. The Hopf-bifurcation analysis is carried out by considering K and r1 as bifurcation parameters. The direction of bifurcating solutions is also determined using the centre manifold arguments. Numerical simulation is carried out to substantiate our analytical findings.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309541
    DOI: 10.1016/j.chaos.2020.110563
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920309541
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110563?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. Fangyuan Hua & Kathryn E. Sieving & Robert J. Fletcher & Chloe A. Wright, 2014. "Increased perception of predation risk to adults and offspring alters avian reproductive strategy and performance," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(3), pages 509-519.
    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. Sönke Eggers & Michael Griesser & Jan Ekman, 2005. "Predator-induced plasticity in nest visitation rates in the Siberian jay (Perisoreus infaustus)," Behavioral Ecology, International Society for Behavioral Ecology, vol. 16(1), pages 309-315, January.
    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. 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).
    2. Yuke Zhang & Xinzhu Meng, 2022. "Dynamics Analysis of a Predator–Prey Model with Hunting Cooperative and Nonlinear Stochastic Disturbance," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    3. Sun, Xiuli, 2023. "Dynamics of a diffusive predator–prey model with nonlocal fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 177(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. Umrao, Anuj Kumar & Roy, Subarna & Tiwari, Pankaj Kumar & Srivastava, Prashant K., 2024. "Dynamical behaviors of autonomous and nonautonomous models of generalist predator–prey system with fear, mutual interference and nonlinear harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    2. Garai, Shilpa & Pati, N.C. & Pal, Nikhil & Layek, G.C., 2022. "Organized periodic structures and coexistence of triple attractors in a predator–prey model with fear and refuge," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Kimberley J. Mathot & Josue David Arteaga-Torres & Anne Besson & Deborah M. Hawkshaw & Natasha Klappstein & Rebekah A. McKinnon & Sheeraja Sridharan & Shinichi Nakagawa, 2024. "A systematic review and meta-analysis of unimodal and multimodal predation risk assessment in birds," Nature Communications, Nature, vol. 15(1), pages 1-15, December.
    4. 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).
    5. Nirapada Santra & Sudeshna Mondal & Guruprasad Samanta, 2022. "Complex Dynamics of a Predator–Prey Interaction with Fear Effect in Deterministic and Fluctuating Environments," Mathematics, MDPI, vol. 10(20), pages 1-38, October.
    6. 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).
    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. 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.
    9. 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).
    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. Helen R. Sofaer & T. Scott Sillett & Susana I. Peluc & Scott A. Morrison & Cameron K. Ghalambor, 2013. "Differential effects of food availability and nest predation risk on avian reproductive strategies," Behavioral Ecology, International Society for Behavioral Ecology, vol. 24(3), pages 698-707.
    13. 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.
    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. Kumbhakar, Ruma & Hossain, Mainul & Pal, Nikhil, 2024. "Dynamics of a two-prey one-predator model with fear and group defense: A study in parameter planes," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    18. Liyun Lai & Zhenliang Zhu & Fengde Chen, 2020. "Stability and Bifurcation in a Predator–Prey Model with the Additive Allee Effect and the Fear Effect," Mathematics, MDPI, vol. 8(8), pages 1-21, August.
    19. Rao, Feng & Kang, Yun, 2023. "Dynamics of a stochastic prey–predator system with prey refuge, predation fear and its carry-over effects," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    20. Matthew Low & Troy Makan & Isabel Castro, 2012. "Food availability and offspring demand influence sex-specific patterns and repeatability of parental provisioning," Behavioral Ecology, International Society for Behavioral Ecology, vol. 23(1), pages 25-34.

    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:143:y:2021:i:c:s0960077920309541. 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.