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Stability and Bifurcation in a Toxicity-Affected Prey-Predator Model with Prey Refuge and Holling Type-II Response | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 تیر 1405 اصل مقاله (2.93 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.67225.3194 | ||
| نویسندگان | ||
| Ramesh Battula1؛ Ramesh Kandala* 2 | ||
| 11. 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. | ||
| 2Department of Mathematics, Anurag University, Venkatapur, Hyderabad-500088, Telangana, India. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Predator-prey model؛ stability؛ toxicity؛ refuge؛ Hopf bifurcation | ||
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آمار تعداد مشاهده مقاله: 3 تعداد دریافت فایل اصل مقاله: 4 |
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