Multi-Stability and Chaotic Behavior in a Three Species Food Web Model with Predation Fear and Weak Allee in Prey

In this paper, we extend the classical Hastings–Powell tri-trophic food chain model by incorporating two ecologically realistic mechanisms: predator-induced fear in prey and a weak Allee effect. A rigorous mathematical analysis is carried out, including positivity, boundedness, dissipativeness, and persistence of solutions, followed by a detailed investigation of all equilibrium points and their local and global stability properties. Through bifurcation analysis, we identify that govern system transitions. Sensitivity analysis using Partial Rank Correlation Coefficients (PRCC) highlights the most influential parameters for prey, predator, and top predator dynamics. Numerical simulations, conducted via MATLAB and MATCONT, further reveal complex dynamical regimes. In particular, variation of the prey-handling time parameter [Formula: see text] drives the system into chaos, as confirmed by a positive maximum Lyapunov exponent (MLE). Importantly, we demonstrate that chaos can be suppressed by strengthening the weak Allee effect ([Formula: see text]) and predator-induced fear ([Formula: see text]). Two-parameter bifurcation diagrams for [Formula: see text], [Formula: see text], and [Formula: see text] provide deeper insights into the combined ecological effects of these parameters. The results, supported with ecological interpretations, show how behavioral responses and Allee effects can regulate chaotic oscillations and promote system stability, offering useful theoretical insights for ecological management and conservation.