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Dynamical behaviour of a two-predator model with prey refuge.

Sahabuddin Sarwardi1, Prashanta Kumar Mandal, Santanu Ray

  • 1Department of Mathematics, Aliah University, DN-41, Sector-V, Salt Lake City, Kolkata 700 091, West Bengal, India. s.sarwardi@gmail.com

Journal of Biological Physics
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Summary

This study models predator-prey dynamics with refuge and competition, analyzing stability and bifurcations to understand ecological system behavior and predict population changes.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Ecological models are crucial for understanding population dynamics.
  • Predator-prey interactions are fundamental to ecosystem stability.
  • Incorporating prey refuge and inter-predator competition adds complexity to ecological models.

Purpose of the Study:

  • To analyze a three-component ecological model with one prey and two predator populations.
  • To investigate the impact of a Holling type II response and prey refuge on population dynamics.
  • To examine predator competition for food and shelter and its effect on system stability and bifurcations.

Main Methods:

  • Development of a mathematical model for a three-component ecological system.
  • Analysis of model stability and bifurcations using mathematical techniques.
  • Determination of threshold parameter values for equilibrium feasibility and stability.
  • Investigation of parameter ranges for different bifurcation types.
  • Numerical simulations to validate model predictions.

Main Results:

  • The study thoroughly analyzes the mathematical features of the model, including stability and bifurcations.
  • Threshold values for key parameters governing feasibility and stability of equilibria were determined.
  • Specific parameter ranges were identified that lead to various types of bifurcations.
  • Numerical illustrations confirmed the model's applicability and the significance of the findings.

Conclusions:

  • The developed model provides insights into complex predator-prey dynamics with refuge and competition.
  • Stability analysis and bifurcation theory are essential tools for understanding ecological system behavior.
  • The findings contribute to predicting population dynamics and ecosystem responses under varying conditions.