Role of Prey Refuge in Predator-Prey Dynamics with Nonlinear Functional Responses: A Mathematical Approach

Notice

This is an unedited manuscript accepted for publication and provided as an Article in Press for early access at the author’s request. The article will undergo copyediting, typesetting, and galley proof review before final publication. Please be aware that errors may be identified during production that could affect the content. All legal disclaimers of the journal apply.

Year : 2025 | Volume : 13 | 03 | Page : –
    By

    Surabhi Pareek,

  • Randhir Singh Baghel,

  1. Research Scholar, Department of Mathematics, Poornima University, Jaipur, Rajasthan, India
  2. Associate Professor, Department of Mathematics, Poornima University, Jaipur, Rajasthan, India

Abstract

The Beddington-DeAnglis and Holling type II functional response with prey refuge are used in this study to propose and assess a prey-predator system. This study looks at the ecological effects of prey refuge and how it affects predator-prey relationships, highlighting how functional responses influence population dynamics. The dynamical behavior of the model has been shown, which consist the existence of positivity, boundedness, local stability, and global stability. In addition, stability is derived using the Routh-Hurwitz criterion. The effect of the attack rate of generalist predators on specialist predators, the biological effect of the attack rate and the inhibitory effect are discussed. Hopf bifurcation is discussed with carrying capacity . Moreover, the Center Manifold theorem has been used to establish the stability of non-hyperbolic equilibrium sites. Simulations are carried out using MATLAB’s ODE45 solver for numerical validation and to see the model’s dynamic behavior. These findings validate the theoretical theory and provide examples of a range of dynamical situations, such as oscillatory behavior and stability transitions, which is a powerful approach to exploring the dynamic behavior of ecological models. Numerical findings are also provided to demonstrate our analysis. Lastly, conclusion has been given. With potential uses in conservation biology and resource management, the study adds to the body of literature on ecological modeling by offering a sophisticated method for examining intricate predator-prey relationships. Overall, by providing a sophisticated framework for comprehending intricate predator-prey dynamics, this study advances the field of ecological modeling. The results offer insights into how behavioral adaptations and ecological restrictions might impact predator-prey interactions, which may find use in conservation biology and resource management.

Keywords: Prey-predator system, Boundedness, Stability, Global stability, Bifurcation, Center manifold theorem.

aWQ6MjA5Njg4fGZpbGVuYW1lOjA4ZTRlNDZhLWZpLXBuZy53ZWJwfHNpemU6dGh1bWJuYWls
How to cite this article:
Surabhi Pareek, Randhir Singh Baghel. Role of Prey Refuge in Predator-Prey Dynamics with Nonlinear Functional Responses: A Mathematical Approach. Journal of Polymer and Composites. 2025; 13(03):-.
How to cite this URL:
Surabhi Pareek, Randhir Singh Baghel. Role of Prey Refuge in Predator-Prey Dynamics with Nonlinear Functional Responses: A Mathematical Approach. Journal of Polymer and Composites. 2025; 13(03):-. Available from: https://journals.stmjournals.com/jopc/article=2025/view=209693


References

  1. Baghel RS, Dhar J. Pattern formation in three species food web model in spatiotemporal domain with Beddington-DeAngelis functional response. Nonlinear Anal Model Control. 2014;19(2):155–71.
  2. Baghel RS, Dhar J, Jain R. Bifurcation and spatial pattern formation in spreading of disease with incubation period in a phytoplankton dynamics. Electron J Differ Equ. 2012;2012(21):1–12.
  3. Dhar J, Baghel RS. Role of dissolved oxygen on the plankton dynamics in spatiotemporal domain. Model Earth Syst Environ. 2016;2(1):6.
  4. Ma Z, Wang S, Wang T, Tang H. Stability analysis of prey-predator system with Holling type functional response and prey refuge. Adv Differ Equ. 2017;2017:1–12.
  5. Jabr EAA-H, Bahlool DK. The dynamics of a food web system: Role of a prey refuge depending on both species. Iraqi J Sci. 2021;639–57.
  6. Jawad S, Naji RK. The influence of stage structure and prey refuge on the stability of the predator-prey model. Int J Eng Manuf. 2022;3:51–9.
  7. Kar TK. Modelling and analysis of a harvested prey-predator system incorporating a prey   J Comput Appl Math. 2006;185(1):19–33.
  8. Holt RD. Food webs in space: On the interplay of dynamic instability and spatial processes. Ecol Res. 2002; 17:261–73.
  9. Nath B, Kumari N, Kumar V, Das KP. Refugia and Allee effect in prey species stabilize chaos in a tri-trophic food chain model. Differ Equ Dyn Syst. 2019;1–27
  10. Kumar V, Kumari N. Bifurcation study and pattern formation analysis of a tri-trophic food         chain model with group defense and Ivlev-like nonmonotonic functional response. Chaos    Solitons Fractals. 2021; 147:110964.
  11. Upadhyay RK, Banerjee M, Parshad R, Raw SN. Deterministic chaos versus stochastic  oscillation in a prey-predator-top predator model. Math Model Anal. 2011;16(3):343–64.
  12. Upadhyay RK, Thakur NK, Rai V. Diffusion-driven instabilities and spatiotemporal patter aquatic predator-prey system with Beddington-DeAngelis type functional response. Int JBifurcation Chaos. 2011;21(3):663–84.
  13. Thakur NK. Turing and non-Turing patterns in diffusive plankton model. Comput Ecol   Softw.  2015;5(1):16.
  14. Upadhyay RK, Naji RK. Dynamics of a three-species food chain model with Crowley-Martin type functional response. Chaos Solitons Fractals. 2009;42(3):1337–46.
  15. Zhao M, Lv S. Chaos in a three-species food chain model with a Beddington-DeAngelis  functional response. Chaos Solitons Fractals. 2009;40(5):2305–16.
  16. Upadhyay RK, Thakur NK, Dubey B. Nonlinear non-equilibrium pattern formation in a spatial aquatic system: Effect of fish predation. J Biol Syst. 2010;18(1):129–59.
  17. Baghel RS. Dynamical behaviour changes in response to various functional responses:  Temporal and spatial plankton system. Iran J Sci. 2023;47(2):445–55.
  18. Baghel RS, Dhar J, Jain R. Analysis of a spatiotemporal phytoplankton dynamics: Higher  order stability and pattern formation. World Acad Sci Eng Technol. 2011; 60:1406–12.
  19. Kumari S, Upadhyay RK. Dynamics comparison between non-spatial and spatial system of the plankton-fish interaction model. Nonlinear Dyn. 2020;99(3):2479–50.
  20. Baghel RS. Spatiotemporal dynamics of toxin-producing phytoplankton–zooplankton interactions with Holling Type II functional responses. Results Control Optim. 2024; 17:100478.
  21. Callahan TK, Knobloch E. Pattern formation in three-dimensional reaction-diffusion systems. Physica D Nonlinear Phenom. 1999;132(3):339–62.
  22. Rai V, Upadhyay RK. Chaotic population dynamics and biology of the top-predator. Chaos Solitons Fractals. 2004;21(5):1195–204.
  23. Baghel RS, Dhar J, Jain R. Bifurcation and spatial pattern formation in spreading of disease with incubation period in a phytoplankton dynamic. Electron J Differ Equ. 2012;2012(21):1–12.
  24. Baghel RS, Dhar J, Jain R. Higher order stability analysis of a spatial phytoplankton dynamics: bifurcation, chaos, and pattern formation. Int J Math Model Simul Appl. 2012; 5:113–27.
  25. Odhiambo F, Aminer T, Okelo B, Manyala J. Dynamical analysis of prey refuge effects on the stability of Holling Type III four-species predator-prey system. Results Control Optim.  2024;100390.
  26. Maionchi DO, Reis SFD, Aguiar MAMD. Chaos and pattern formation in a spatial tri-trophic food chain. Ecol Model. 2006;191(2):291–303.
  27. Baghel RS, Pareek S. Influence of nanoparticles on the spatiotemporal dynamics of phytoplankton–zooplankton interaction system. Int J Biomathematics. 2024;2450131.
  28. Baghel RS, Pareek S. A complex dynamical study of spatiotemporal plankton-fish interaction with effects of harvesting. Iran J Sci. 2024;48(2):409–21.
  29. Agarwal K, Baghel RS, Parmar A, et al. Jeffery Slip fluid flow with the magnetic dipole effect over a melting or permeable linearly stretching sheet. Int J Appl Comput Math. 2024; 10:5.
Ahead of Print Subscription Original Research
Volume 13
03
Received 25/11/2024
Accepted 08/02/2025
Published 01/05/2025
Publication Time 157 Days
Total Visits: 30


My IP

PlumX Metrics