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Discontinuity, Nonlinearity, and Complexity 14(1) (2025) 145--161 | DOI:10.5890/DNC.2025.03.009

Krishna Pada Das$^1$, Sanjukta Pramanik$^2$, Palash Mondal$^3$, Santanu Biswas$^4$, Seema Sarkar(Mondal)$^5$, Goutam Panigrahi$^5$

$^1$ Department of Mathematics, Mahadevanada Mahavidyalaya Monirampore, P.O.-Barrackpore, Kolkata 700120, India

$^2$ Department of Mathematics, Chakdaha College, Chakdaha, West Bengal, Pin - 741222, India

$^3$ Sankarpur High Madrasah(HS), District - Murshidabad, Pin - 742159, West Bengal, India

$^4$ Department Of Mathematics, Ramakrishna Mission Vivekananda Centenary College, Rahara

$^5$ Department of Mathematics, National Institute of technology Durgapur, Durgapur, West Bengal, India

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Abstract

Controlling and regulating chaotic dynamics in predator-prey systems have become an attractive field of investigation for researchers in the arena of mathematical biology. We claim Allee effect to be one such measure of controlling chaos in an eco-epidemiological model subject to environmental toxicity. In our investigation, we have established mathematical properties such an existence of points of equilibria and their local stablitiy analysis. Hopf bifurcation analysis have been examined and established followed by permanence of the model taken under consideration. Likewise, we have demonstrated global stability of the interior equilibrium point. Infection parameter $\beta$ and Allee parameter $\theta$ serve the purpose of control parameters. The numerical simulation indicates that with gradual decrease in the value of infection parameter, the system becomes more stable. On the other hand, with increasing value of Allee parameter, the system fetches stability from chaotic behaviour of the system.The analytical findings have been strongly validated by extensive numerical simulation in this article.

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