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Discontinuity, Nonlinearity, and Complexity 14(1) (2025) 227--242 | DOI:10.5890/DNC.2025.03.014

Abhishek Sarkar$^{1}$, Kulbhushon Agnihotri$^{1}$, Ani Jain$^{2}$, Parimita Roy$^{2}$, Prodip Roy$^{3}$, Krishna Pada Das$^{3}$

$^{1}$ Department of Applied Science And Humanities, Shaheed Bhagat Singh State University, Ferozpore, Punjab, India

$^{2}$ Department of Mathematics, Thapar Institute of engineering and technology, Punjab, India

$^{3}$ Department of Mathematics, Mahadevananda Mahavidyalaya, monirampure, Barrackpore, Kolkata, India

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Abstract

Tri-trophic food chains represent intricate ecological systems, wherein predators, prey, and primary producers engage in complex interactions. Studying the dynamics of such systems is of paramount importance for understanding the delicate balance of ecosystems and their responses to external perturbations. In this paper, we delve into the intricate dynamics of a tri-trophic food chain model, incorporating the influential Holling Type II functional response, insights from the Hasting and Powell model, and the inclusion of prey and intermediate predator harvesting effects. By analyzing equilibrium points, assessing local and global stability, exploring Hopf bifurcations, chaotic, limit cycle, stability, period-doubling and conducting numerical simulations, we aim to unravel the rich dynamics that arise from these ecological interactions.

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