Stability and Bifurcation in a Toxicity-Affected Prey-Predator Model with Prey Refuge and Holling Type-II Response

Articles in Press

Document Type : Research Paper

Authors

1 1. Department of Mathematics, AVN Institute of Engineering and Technology, Koheda Road, Ibrahimpatnam, Hyderabad-501510, Telangana, India. 2. Department of Mathematics, Anurag University, Venkatapur, Hyderabad-500088, Telangana, India.

2 Department of Mathematics, Anurag University, Venkatapur, Hyderabad-500088, Telangana, India.

Abstract

This study explores the stability and bifurcation dynamics of a toxicity-affected prey-predator model incorporating prey refuge and a Holling Type-II functional response. The model consists of two nonlinear differential equations in which prey populations increase logistically, and the predator functional response is modified by the presence of prey refuge, making the predators' effective predation rate lower. Both species are affected by toxicity, which changes the dynamics of the system by reducing prey reproduction and increasing predator mortality. This model incorporates the combined effects of prey refuge and toxicity within predator-prey interactions, thereby providing a more realistic ecological framework for studying species dynamics under environmental stress. The study establishes the positivity and boundedness of solutions, thereby affirming ecological viability. The local and global stability of the equilibria are analyzed using Lyapunov functions and standard stability criteria. Furthermore, conditions for Hopf bifurcation are established to ascertain the emergence of periodic oscillations. Hopf bifurcation analysis is performed numerically using MATLAB to investigate the impact of toxicity levels and prey refuge on system stability and species persistence. The numerical simulations corroborate the analytical findings, providing insights into the ecological ramifications of environmental toxicity and the protective strategies employed by prey populations. By providing a theoretical framework for upcoming research on ecosystem sustainability under environmental perturbations, this work advances our knowledge of toxin-mediated predator-prey interactions.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 10 July 2026

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History

  • Receive Date: 09 May 2025
  • Revise Date: 13 May 2026
  • Accept Date: 09 July 2026

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