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Bifurcations and organized structures in a predator-prey model with hunting cooperation

Author

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  • Pati, N.C.
  • Layek, G.C.
  • Pal, Nikhil

Abstract

We report new organized structures in bi-parameter space for a nonlinear discrete predator-prey model with hunting cooperation. The intrinsic hunting cooperation among predator populations alters the dynamical behaviors of the model significantly. Especially, the stable periodic organized structures, viz. the Arnold tongues and shrimp-shaped structures in quasi-periodic and chaotic regimes exist near the boundary of Neimark-Sacker bifurcation for moderate values of the hunting cooperation parameter. Interestingly, these regular structures lead to different period-adding sequences. The transition to chaos via period-bubbling cascade near the inner boundaries of the shrimp-shaped structures is obtained. Shrimp structures maintain the universality of period 3-times self-similarity. Also, the coexistence of multiple periodic cycles and chaotic attractors with fractal basin boundaries are found owing to the hunting cooperation among the predators.

Suggested Citation

  • Pati, N.C. & Layek, G.C. & Pal, Nikhil, 2020. "Bifurcations and organized structures in a predator-prey model with hunting cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305804
    DOI: 10.1016/j.chaos.2020.110184
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    Citations

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    Cited by:

    1. N. C. Pati, 2023. "Bifurcations and multistability in a physically extended Lorenz system for rotating convection," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-15, August.
    2. Hossain, Mainul & Pati, N.C. & Pal, Saheb & Rana, Sourav & Pal, Nikhil & Layek, G.C., 2021. "Bifurcations and multistability in a food chain model with nanoparticles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 808-825.
    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. Uddin, Md. Jasim & Rana, Sarker Md. Sohel & Işık, Seval & Kangalgil, Figen, 2023. "On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    5. 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).
    6. Vishwakarma, Krishnanand & Sen, Moitri, 2021. "Role of Allee effect in prey and hunting cooperation in a generalist predator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 622-640.
    7. Shang, Zuchong & Qiao, Yuanhua & Duan, Lijuan & Miao, Jun, 2021. "Bifurcation analysis in a predator–prey system with an increasing functional response and constant-yield prey harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 976-1002.
    8. Pandey, Soumik & Ghosh, Uttam & Das, Debashis & Chakraborty, Sarbani & Sarkar, Abhijit, 2024. "Rich dynamics of a delay-induced stage-structure prey–predator model with cooperative behaviour in both species and the impact of prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 49-76.
    9. Chou, Yen-hsi & Chow, Yunshyong & Hu, Xiaochuan & Jang, Sophia R.-J., 2021. "A Ricker–type predator–prey system with hunting cooperation in discrete time," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 570-586.
    10. Yanfei Du & Ben Niu & Junjie Wei, 2021. "Dynamics in a Predator–Prey Model with Cooperative Hunting and Allee Effect," Mathematics, MDPI, vol. 9(24), pages 1-40, December.
    11. Chen, Mengxin & Srivastava, Hari Mohan, 2023. "Stability of bifurcating solution of a predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    12. Bozkurt, Fatma & Yousef, Ali & Bilgil, Halis & Baleanu, Dumitru, 2023. "A mathematical model with piecewise constant arguments of colorectal cancer with chemo-immunotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    13. 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.
    14. Hossain, Mainul & Kumbhakar, Ruma & Pal, Nikhil, 2022. "Dynamics in the biparametric spaces of a three-species food chain model with vigilance," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    15. Tian, Yuan & Li, Huanmeng & Sun, Kaibiao, 2024. "Complex dynamics of a fishery model: Impact of the triple effects of fear, cooperative hunting and intermittent harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 31-48.

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