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Rich dynamics of a delay-induced stage-structure prey–predator model with cooperative behaviour in both species and the impact of prey refuge

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  • Pandey, Soumik
  • Ghosh, Uttam
  • Das, Debashis
  • Chakraborty, Sarbani
  • Sarkar, Abhijit

Abstract

The prey–predator interaction between organisms living in an ecosystem is greatly affected by the cooperation among the species as well as immature prey refuge in presence of time delay. This study has developed and analysed a stage-structured prey–predator model that includes refuge behaviour for prey and two types of cooperative behaviours, namely cooperative behaviour among prey as well as cooperative behaviour among predators, in addition to gestational delay. The presence of Saddle–node, Transcritical, and Hopf-bifurcations is explained by analytically and numerically. We examine the model parameter’s sensitivity to determine the species’ favourable and unfavourable impacts and to identify the most significant parameters. The dynamics of delay and non-delay systems are compared, and we recognise that a consistent increase in time delay causes chaotic oscillations with period-doubling fluctuations which can be regulated by the refuge for immature prey. However, we demonstrate that the immature prey refuge destabilises the system in absence of time delay while it acts as a control parameter in presence of delay. Finally, we wrap up the paper by highlighting the key biological implications of the numerical and analytical findings.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:216:y:2024:i:c:p:49-76
    DOI: 10.1016/j.matcom.2023.09.002
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    References listed on IDEAS

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    1. 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).
    2. Jiao, Jianjun & Chen, Lansun & Cai, Shaohong, 2009. "A delayed stage-structured Holling II predator–prey model with mutual interference and impulsive perturbations on predator," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1946-1955.
    3. 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.
    4. Kundu, Soumen & Maitra, Sarit, 2018. "Dynamics of a delayed predator-prey system with stage structure and cooperation for preys," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 453-460.
    5. Mondal, Bapin & Ghosh, Uttam & Rahman, Md Sadikur & Saha, Pritam & Sarkar, Susmita, 2022. "Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 111-135.
    6. Capone, F. & Carfora, M.F. & De Luca, R. & Torcicollo, I., 2019. "Turing patterns in a reaction–diffusion system modeling hunting cooperation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 172-180.
    7. Jana, Soovoojeet & Chakraborty, Milon & Chakraborty, Kunal & Kar, T.K., 2012. "Global stability and bifurcation of time delayed prey–predator system incorporating prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 57-77.
    8. 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.
    9. 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.
    10. Yongzhen, Pei & Changguo, Li & Lansun, Chen, 2009. "Continuous and impulsive harvesting strategies in a stage-structured predator–prey model with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 2994-3008.
    11. Ghosh, Sinchan & Basir, Fahad Al & Chowdhury, Ganesh & Bhattacharya, Sabyasachi & Ray, Santanu, 2021. "Is the primary helper always a key group for the dynamics of cooperative birds? A mathematical study on cooperative breeding birds," Ecological Modelling, Elsevier, vol. 459(C).
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