Deterministic‐Stochastic Analysis of a Two Species Predator‐Prey System Under the Influence of Intraspecific Competition and Fear Effect

ABSTRACT Based on a two‐dimensional dynamical ecological framework, this study presents a modified predator‐prey model that incorporates intraspecific competition, predator‐induced fear in prey, and environmental stochasticity. The prey's reproduction rate is modeled as a decreasing function of predator density and fear intensity, while predator dynamics follow a modified Holling type II functional response. Analytical investigations establish conditions for the existence and stability of equilibria, as well as persistence and bifurcations, including transcritical and Hopf types. Numerical simulations reveal that higher fear intensity or intraspecific competition stabilizes dynamics by suppressing oscillations, whereas their reduction leads to limit cycles via supercritical or subcritical Hopf bifurcations. Two‐parameter bifurcation analysis uncovers generalized Hopf bifurcations and bistability. Stochastic simulations with Gaussian white noise indicate that low‐intensity fluctuations preserve coexistence, while stronger noise destabilizes the system. Global sensitivity analysis identifies the most influential parameters affecting population dynamics. A brief comparative discussion shows that excluding mechanisms such as noise simplifies the system and reduces its dynamical complexity.