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Comparative Study of Deterministic and Stochastic Predator Prey System Incorporating a Prey Refuge

In: Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics

Author

Listed:
  • Anal Chatterjee

    (Barrackpore Rastraguru Surendranath College, North 24 Parganas, Department of Mathematics)

  • Samares Pal

    (University of Kalyani, Department of Mathematics)

Abstract

The goal of this research is to investigate the dynamical behaviour of a predator-prey system with Holling II functional response in a systematic way. The system’s various dynamical behaviours have been investigated, with the prey refuge being proportional to both species. The proposed model has been tested in the absence and presence of environmental disturbances. In a deterministic system, the permanence, local stability, transcritical bifurcation and Hopf bifurcation are investigated under various parametric conditions. The significant parameters ranges in which the system exhibits a Hopf bifurcation are examined. Furthermore, we observe that if the white noise intensity is kept below a particular threshold value, the deterministic control approach is equally valid in case of environmental disturbances. Finally, we ran a sufficient numerical simulation to validate our theoretical results.

Suggested Citation

  • Anal Chatterjee & Samares Pal, 2023. "Comparative Study of Deterministic and Stochastic Predator Prey System Incorporating a Prey Refuge," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics, pages 73-98, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-33050-6_5
    DOI: 10.1007/978-3-031-33050-6_5
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