IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v178y2024ics0960077923012675.html
   My bibliography  Save this article

Bistability in modified Holling II response model with harvesting and Allee effect: Exploring transitions in a noisy environment

Author

Listed:
  • Mandal, Sayan
  • Sk, Nazmul
  • Tiwari, Pankaj Kumar
  • Chattopadhyay, Joydev

Abstract

Here, we explore the complex dynamics of a predator–prey system with a modified Holling type II functional response and the Allee effect that accounts for a reduced hunting efficiency due to intra-predator interactions. Besides the growth due to focal prey, the predator population follows a Beverton–Holt-like reproduction due to the alternative food sources. The model also considers the impact of harvesting on the predator population, reflecting economic interests in biological resource exploitation. We systematically investigate key aspects, including solution’s positivity, system’s equilibria, stability analysis, and various type of bifurcation. The model is extended to its stochastic version; conditions for the extinction as well as persistence of species are derived. All the theoretical findings are validated with numerical examples. In the deterministic scenario, the Allee effect, harvesting intensity, and the growth in predators due to external food sources exhibit intricate dynamics, such as Hopf, saddle–node (LP) and transcritical bifurcations; we also observe bistable behavior of the system. Notably, less growth in predators due to the other food sources results in extinction, while low intensity of Allee effect leads to bistability, where initial population size matters. A higher Allee effect reduces the region of stability generated by the harvesting effort and the predators’ growth due to additional foods. The stochastic system uncovers diverse transitions in scenarios with high noise intensity, affecting bistability occurred for lower noise intensity. Overall, this study provides valuable insights into predator–prey dynamics, with practical implications for the ecological conservation and resource management.

Suggested Citation

  • Mandal, Sayan & Sk, Nazmul & Tiwari, Pankaj Kumar & Chattopadhyay, Joydev, 2024. "Bistability in modified Holling II response model with harvesting and Allee effect: Exploring transitions in a noisy environment," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923012675
    DOI: 10.1016/j.chaos.2023.114365
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923012675
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114365?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. de Souza, Silvio L.T. & Batista, Antonio M. & Caldas, Iberê L. & Viana, Ricardo L. & Kapitaniak, Tomasz, 2007. "Noise-induced basin hopping in a vibro-impact system," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 758-767.
    2. Xu, Chaoqun & Yuan, Sanling & Zhang, Tonghua, 2018. "Sensitivity analysis and feedback control of noise-induced extinction for competition chemostat model with mutualism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 891-902.
    3. Peng, Yahong & Zhang, Tonghua, 2016. "Turing instability and pattern induced by cross-diffusion in a predator-prey system with Allee effect," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 1-12.
    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. Bashkirtseva, I. & Ryashko, L., 2019. "Stochastic sensitivity analysis of chaotic attractors in 2D non-invertible maps," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 78-84.
    2. de Souza, S.L.T. & Batista, A.M. & Baptista, M.S. & Caldas, I.L. & Balthazar, J.M., 2017. "Characterization in bi-parameter space of a non-ideal oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 224-231.
    3. Xiong Wang & Akif Akgul & Sezgin Kacar & Viet-Thanh Pham, 2017. "Multimedia Security Application of a Ten-Term Chaotic System without Equilibrium," Complexity, Hindawi, vol. 2017, pages 1-10, November.
    4. Irina Bashkirtseva, 2021. "Controlling Stochastic Sensitivity by Feedback Regulators in Nonlinear Dynamical Systems with Incomplete Information," Mathematics, MDPI, vol. 9(24), pages 1-12, December.
    5. Liu, Qun & Jiang, Daqing, 2020. "Threshold behavior in a stochastic SIR epidemic model with Logistic birth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    6. Li, Qiang & Liu, Zhijun & Yuan, Sanling, 2019. "Cross-diffusion induced Turing instability for a competition model with saturation effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 64-77.
    7. Hua Liu & Yong Ye & Yumei Wei & Weiyuan Ma & Ming Ma & Kai Zhang, 2019. "Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay," Complexity, Hindawi, vol. 2019, pages 1-14, November.
    8. Richter, Hendrik, 2008. "On a family of maps with multiple chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 559-571.
    9. Liu, Yanwei & Zhang, Tonghua & Liu, Xia, 2020. "Investigating the interactions between Allee effect and harvesting behaviour of a single species model: An evolutionary dynamics approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    10. Guo, Gaihui & Qin, Qijing & Cao, Hui & Jia, Yunfeng & Pang, Danfeng, 2024. "Pattern formation of a spatial vegetation system with cross-diffusion and nonlocal delay," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    11. Liu, Guodong & Meng, Xinzhu, 2019. "Optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    12. Wang, Fatao & Yang, Ruizhi & Zhang, Xin, 2024. "Turing patterns in a predator–prey model with double Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 170-191.
    13. Chen, Jianxin & Zhang, Tonghua & Zhou, Yong-wu, 2021. "Stochastic sensitivity and dynamical complexity of newsvendor models subject to trade credit," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 471-486.
    14. Yu Mu & Zuxiong Li & Huili Xiang & Hailing Wang, 2019. "Dynamical Analysis of a Stochastic Multispecies Turbidostat Model," Complexity, Hindawi, vol. 2019, pages 1-18, January.
    15. 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.
    16. Zhang, Feifan & Sun, Jiamin & Tian, Wang, 2022. "Spatiotemporal pattern selection in a nontoxic-phytoplankton - toxic-phytoplankton - zooplankton model with toxin avoidance effects," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    17. Tang, Xiaosong & Zhang, Xiaoyu & Liu, Yiting & Li, Wankun & Zhong, Qi, 2023. "Global stability and Turing instability deduced by cross-diffusion in a delayed diffusive cooperative species model," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    18. Saifuddin, Md. & Biswas, Santanu & Samanta, Sudip & Sarkar, Susmita & Chattopadhyay, Joydev, 2016. "Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 270-285.
    19. Yan, Shuixian & Jia, Dongxue & Zhang, Tonghua & Yuan, Sanling, 2020. "Pattern dynamics in a diffusive predator-prey model with hunting cooperations," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    20. Xu, Chaoqun, 2020. "Probabilistic mechanisms of the noise-induced oscillatory transitions in a Leslie type predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 137(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:chsofr:v:178:y:2024:i:c:s0960077923012675. 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.