IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v199y2025ip1s0960077925006071.html

Trade-off dynamics of predator–prey system incorporating variable carrying capacity and wind effect

Author

Listed:
  • Dai, Chuanyu
  • Wang, Qinglong
  • Liu, Zhijun
  • Yan, Qian

Abstract

In ecosystems, predators are exposed to the risk of getting injured while hunting dangerous prey. As a result, they need to make a “trade-off” between securing food and ensuring their own safety. This article aims to explore the predators’ trade-off behavior by introducing a new function that reflects predators’ loss, and establishes a two-dimensional system for prey and predator interaction concerning variable carrying capacity and wind flow. Our analysis primarily focuses on the autonomous system’s positivity and boundedness. Also, the existence and local stability of possible equilibrium points are addressed. Meanwhile, the system exhibits two kinds of bifurcation phenomena (the Hopf and transcritical bifurcations). It is worth mentioning that the seasonality in variable carrying capacity and wind flow’s fluctuation may lead to complex dynamic behavior, which drives us to thoroughly discuss the positivity, boundedness and existence of the periodic solution. Then the numerical simulations are conducted to confirm the viability of the theoretical outcomes, offering strong evidence for the practical implementation. Finally, the presence of random fluctuations modifying the dynamics of the autonomous system is also analyzed numerically.

Suggested Citation

  • Dai, Chuanyu & Wang, Qinglong & Liu, Zhijun & Yan, Qian, 2025. "Trade-off dynamics of predator–prey system incorporating variable carrying capacity and wind effect," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p1:s0960077925006071
    DOI: 10.1016/j.chaos.2025.116594
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925006071
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116594?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. 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).
    2. Bhutia, Lakpa Thendup & Biswas, Samir & Das, Esita & Kar, Tapan Kumar & Bhunia, Bidhan, 2025. "Evolution of Turing patterns of a predator–prey system with variable carrying capacity and harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    3. 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).
    4. Valenti, D. & Fiasconaro, A. & Spagnolo, B., 2004. "Stochastic resonance and noise delayed extinction in a model of two competing species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 477-486.
    5. Sajan, & Kumar Choudhary, Kapil & Dubey, Balram, 2023. "A non-autonomous approach to study the impact of environmental toxins on nutrient-plankton system," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    6. 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).
    7. Pati, N.C. & Ghosh, Bapan, 2022. "Delayed carrying capacity induced subcritical and supercritical Hopf bifurcations in a predator–prey system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 171-196.
    8. Yao, Haiqing & Wang, Qinglong & Liu, Zhijun, 2025. "Dynamical behaviors of a generalist predator–prey system with Allee and wind effects in deterministic or stochastic environment," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    9. Sk, Nazmul & Tiwari, Pankaj Kumar & Pal, Samares, 2022. "A delay nonautonomous model for the impacts of fear and refuge in a three species food chain model with hunting cooperation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 136-166.
    10. 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).
    11. Pal, Saheb & Pal, Nikhil, 2025. "Modelling the wind effect in predator–prey interactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 75-90.
    12. Bhunia, Bidhan & Ghorai, Santu & Kar, Tapan Kumar & Biswas, Samir & Bhutia, Lakpa Thendup & Debnath, Papiya, 2023. "A study of a spatiotemporal delayed predator–prey model with prey harvesting: Constant and periodic diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    13. Bhargava, Masoom & Dubey, Balram, 2024. "Trade-off and chaotic dynamics in a two-prey one-predator model with refuge, environmental noise and seasonal effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 218-245.
    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. Mandal, Sayan & Samanta, Sudip & Tiwari, Pankaj Kumar & Upadhyay, Ranjit Kumar, 2025. "Bifurcation analysis and exploration of noise-induced transitions of a food chain model with Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 313-338.
    2. Roy, Subarna & Tiwari, Pankaj Kumar, 2025. "Bistability in a predator–prey model characterized by the Crowley–Martin functional response: Effects of fear, hunting cooperation, additional foods and nonlinear harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 274-297.
    3. Zhuo, Xiao-jing & Guo, Yong-feng & Qi, Jing-yan & Wang, Qian-qian, 2024. "Stationary distribution and mean extinction time in a generalist prey–predator model driven by Lévy noises," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    4. 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.
    5. Bhutia, Lakpa Thendup & Biswas, Samir & Das, Esita & Kar, Tapan Kumar & Bhunia, Bidhan, 2025. "Evolution of Turing patterns of a predator–prey system with variable carrying capacity and harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    6. Rashi, & Singh, Suruchi & Umrao, Anuj Kumar & Singh, Harendra Pal & Srivastava, Prashant K., 2025. "Cooperation and harvesting-induced delays in a predator–prey model with prey fear response: A crossing curves approach," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    7. Tian, Yuan & Yan, Xinrui & Sun, Kaibiao, 2024. "Dual effects of additional food supply and threshold control on the dynamics of a Leslie–Gower model with pest herd behavior," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    8. Yao, Haiqing & Wang, Qinglong & Liu, Zhijun, 2025. "Dynamical behaviors of a generalist predator–prey system with Allee and wind effects in deterministic or stochastic environment," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    9. Xue, Yalong & Chen, Shengjiang & Xu, Lili & Chen, Fengde, 2025. "Fear-driven gregariousness and survival: Modeling bidirectional feedbacks and seasonality in a generalist predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    10. Wang, Min & Fang, Yuwen & Luo, Yuhui & Yang, Fengzao & Zeng, Chunhua & Duan, Wei-Long, 2019. "Influence of non-Gaussian noise on the coherent feed-forward loop with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 46-55.
    11. Chun Zhang & Tao Yang & Shi-Xian Qu, 2021. "Impact of time delays and environmental noise on the extinction of a population dynamics model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(11), pages 1-16, November.
    12. Ojha, Archana & Mandal, Sayan & Singh, Ravikant & Thakur, Nilesh Kumar & Tiwari, Pankaj Kumar, 2025. "Predator–prey dynamics in autonomous and nonautonomous settings: Impacts of anti-predator behavior, refuge, and additional food," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    13. Li, Zhenlei & Zhang, Yue, 2024. "Dynamic analysis of a fast slow modified Leslie–Gower predator–prey model with constant harvest and stochastic factor," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 474-499.
    14. Ding, Linglong & Zhang, Xuebing & Lv, Guangying, 2024. "Dynamics of a plankton community with delay and herd-taxis," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    15. Das, Dipam & Bhattacharjee, Debasish, 2025. "An investigation into the impact of odour: A dynamical study of two predators and one prey model, taking into account both integer order and fractional order derivatives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 341-368.
    16. Morozov, Andrew Yu. & Almutairi, Dalal & Petrovskii, Sergei V. & Lai, Ying-Cheng, 2023. "Long transients in discontinuous time-discrete models of population dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    17. Fayezi, Sajad & Zomorrodi, Maryam, 2025. "Navigating the multiplicity of sustainability policies in agribusiness supply networks: The role of policy brokers and advocates," Food Policy, Elsevier, vol. 136(C).
    18. Paul, Biswajit & Sikdar, Gopal Chandra & Ghosh, Uttam, 2025. "Effect of fear and non-linear predator harvesting on a predator–prey system in presence of environmental variability," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 442-460.
    19. Barman, Dipesh & Kumar Upadhyay, Ranjit, 2026. "Impact of carryover and fear-induced delays on population dynamics: A cross-model stability and bifurcation investigation," Applied Mathematics and Computation, Elsevier, vol. 516(C).
    20. Vladislav Soukhovolsky & Anton Kovalev & Yulia Ivanova & Olga Tarasova, 2023. "Autoregression, First Order Phase Transition, and Stochastic Resonance: A Comparison of Three Models for Forest Insect Outbreaks," Mathematics, MDPI, vol. 11(19), pages 1-19, October.

    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:199:y:2025:i:p1:s0960077925006071. 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.