Discontinuity, Nonlinearity, and Complexity 15(3) (2026) 413--426 | DOI:10.5890/DNC.2026.09.009

Mohan Kumar G$^1$, Anupam Priyadarshi$^2$, Abhishek Kumar Singh$^1$

$^1$ Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology-Chennai Campus, Chennai - 600 127, Tamil Nadu, India

$^2$ Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India

Abstract

Biological and behavioral strategies that enhance species survival and population stability play a crucial role in predator–prey interactions within ecological food webs. In this study, we develop and analyze a mathematical model involving two prey species and a single predator, incorporating key ecological mechanisms such as herd behavior, fear effects, prey refuge, intraspecific competition among predators, and the Allee effect in one of the prey species. The predator–prey dynamics are governed by a Holling type II functional response that accounts for herd behavior, where the prey capture rate is proportional to the square root of prey density. We derive equilibrium points to examine system stability and establish the non-negativity and boundedness of solutions. Local stability conditions at the interior equilibrium are analyzed, and bifurcation analyses including transcritical and Hopf bifurcations are carried out to explore the system's dynamic behavior. Numerical simulations support the analytical results, offering insights into species interactions through time-series analysis and one-parameter bifurcation diagrams. The findings emphasize the roles of prey refuge, the Allee effect, and other ecological factors in shaping predator–prey dynamics, contributing to a deeper understanding of ecosystem stability and species persistence.

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