Role of Allee in Controlling Chaotic Dynamics in an Eco-Epidemiological Model with Diffusion

This study presents a novel extension of the classical Rosenzweig–MacArthur predator–prey model by incorporating two predator species and an Allee effect in the prey population, along with an eco-epidemiological interaction between the predators. The resulting system captures complex trophic dynamics where the intermediate predator is suppressed by both direct predation on the prey and a parasitic or infection-like pressure from the top predator. The prey population is subject to Allee-type depensation, influencing its ability to recover at low densities a biologically relevant feature in many real ecosystems. Mathematically, the model is formulated through a set of nonlinear ordinary differential equations, analyzed for equilibrium behavior, local and global stability, and bifurcations. The system is nondimensionalized to reduce parameter redundancy and emphasize key ecological mechanisms. Stability and bifurcation analyses are performed to uncover critical thresholds where the system shifts from stable coexistence to periodic or chaotic behavior. We then examine the spatially explicit system and evaluate the Turing instability conditions for the resulting spatio-temporal dynamics. Numerical simulations, including bifurcation diagrams and Lyapunov exponent computations, validate the analytical findings and demonstrate rich dynamical regimes including stable nodes, limit cycles, and strange attractors. Biologically, the model emphasizes the role of Allee effects, predator interference, and infection-like interactions in shaping population persistence and ecosystem stability. The results underscore the importance of managing interspecies interactions and mortality rates to prevent extinction and chaotic outbreaks. This work contributes to the understanding of nonlinear eco-epidemiological systems and provides a basis for future studies incorporating spatial dynamics or stochasticity.